Free Propagator Research Articles

Thermodynamic properties of a relativistic Bose gas under rigid rotation

We study the thermodynamic properties of a rigidly rotating relativistic Bose gas. First, we derive the solution of the equation of motion corresponding to a rotating complex Klein-Gordon field and determine the free propagator of this model utilizing the Fock-Schwinger proper-time method. Using this propagator, we then obtain the thermodynamic potential of this model in the zeroth and first perturbative level. In addition, we compute the nonperturbative ring contribution to this potential. Our focus is on the dependence of these expressions on the angular velocity, which effectively acts as a chemical potential. Using this thermodynamic potential, we calculate several quantities, including the pressure, angular momentum and entropy densities, heat capacity, speed of sound, and moment of inertia of this rigidly rotating Bose gas as functions of temperature (T), angular velocity (Ω), and the coupling constant (α). We show that certain thermodynamic instabilities appear at high temperatures and large couplings. They are manifested as zero and negative values of the above quantities, particularly the moment of inertia and heat capacity. Zero moment of inertia leads to the phenomenon of supervorticity at certain T or α. Supervortical temperatures (couplings) decrease with increasing coupling (temperature). We also observe superluminal sound velocities at high T and for large α. Published by the American Physical Society 2024

Simple proof that there is no sign problem in path integral Monte Carlo simulations of fermions in one dimension.

It is widely known that there is no sign problem in path integral Monte Carlo (PIMC) simulations of fermions in one dimension. As far as the author is aware, there is no direct proof of this in the literature. This work shows that the sign of the N-fermion antisymmetric free propagator is given by the product of all possible pairs of particle separations, or relative displacements. For a nonvanishing closed-loop product of such propagators, as required by PIMC, all relative displacements from adjacent propagators are paired into perfect squares, and therefore the loop product must be positive, but only in one dimension. By comparison, permutation sampling, which does not evaluate the determinant of the antisymmetric propagator exactly, remains plagued by a low-level sign problem, even in one dimension.

Spacetime metric from quantum-gravity corrected Feynman propagators

Differentiation of the scalar Feynman propagator with respect to the spacetime coordinates yields the metric on the background spacetime that the scalar particle propagates in. Now Feynman propagators can be modified in order to include quantum-gravity corrections as induced by a zero-point length [Formula: see text]. These corrections cause the length element [Formula: see text] to be replaced with [Formula: see text] within the Feynman propagator. In this paper, we compute the metrics derived from both the quantum-gravity free propagators and from their quantum-gravity corrected counterparts. We verify that the latter propagators yield the same spacetime metrics as the former, provided one measures distances greater than the quantum of length [Formula: see text]. We perform this analysis in the case of the background spacetime [Formula: see text] in the Euclidean sector.

Impact of Anomalous Diffusion Phenomenon on Molecular Information Delivery in Bounded Environment.

Through this paper, a three-dimensional molecular communication (MC) inside a cuboid container is considered. Instead of normal diffusion phenomenon, the anomalous diffusion phenomenon is incorporated which enhances the practicability of the model. The Fick's law is re-defined for the considering rectangular coordinate system in which information carrying molecules (ICMs) diffuse anomalously in the environment. The impact of flow of the fluid along the +x direction in the environment is also considered. Moreover, considering free propagator phenomenon, the expressions of spatio-temporal probability density function (PDF) of the ICMs is derived for the considered model. Further, the novel closed-form expressions for first arrival time density (FATD) of the ICM, survival probability (SP) at any time, and its corresponding first arrival probability (FAP) are also derived. Furthermore, the considered MC model is also analyzed in terms of minimum bit-error-rate (BER) using log-likelihood ratio test (LLRT) optimal detector. The derived expressions are verified using MATLAB based particle-based and Monte-Carlo simulations.

Anatomy of path integral Monte Carlo: Algebraic derivation of the harmonic oscillator's universal discrete imaginary-time propagator and its sequential optimization.

The direct integration of the harmonic oscillator path integral obscures the fundamental structure of its discrete, imaginary time propagator (density matrix). This work, by first proving an operator identity for contracting two free propagators into one in the presence of interaction, derives the discrete propagator by simple algebra without doing any integration. This discrete propagator is universal, having the same two hyperbolic coefficient functions for all short-time propagators. Individual short-time propagator only modifies the coefficient function's argument, its portal parameter, whose convergent order is the same as the thermodynamic energy. Moreover, the thermodynamic energy can be given in a closed form for any short-time propagator. Since the portal parameter can be systematically optimized by matching the expansion of the product of the two coefficients, any short-time propagator can be optimized sequentially, order by order, by matching the product coefficient's expansion alone, without computing the energy. Previous empirical findings on the convergence of fourth and sixth-order propagators can now be understood analytically. An eight-order convergent short-time propagator is also derived.

A new version of PyWolf for the propagation of partially coherent light in media other than free space

PyWolf is an open-source software capable of performing numerical simulations of partially coherent light propagation from two-dimensional light sources using parallel computation. In the original version of PyWolf, the graphical user interface (GUI) would only show free-space propagation as the only option for propagating partially coherent light, even though users could add their own source models and other objects such as lenses and apertures, which was recognized by PyWolf's GUI. We introduce here the new version of PyWolf, PyWolf 2.0, which among other improvements, enables users to easily add their own propagation medium, which can be used throughout the simulation in different propagation planes. New version program summaryProgram Title: PyWolfCPC Library link to program files:https://doi.org/10.17632/frjscxypkd.2Developer's repository link:https://github.com/tiagoecmagalhaes/PyWolfLicensing provisions: GPLv3Programming language: PythonSupplementary material: Detailed description of the main changes with an example.Journal reference of previous version: Comput. Phys. Commun. 276 (2022) 108336.Reasons for the new version: In the previous paper [1] describing the original version of PyWolf, the propagation kernel was limited to free space, even though optical elements such as lenses and apertures could be added. For propagation in other media (e.g., turbulent medium), users had to substitute the free space propagation by the desired propagation medium since PyWolf always uses the same propagator, which is present in a single Python script.Summary of revisions: Propagation model selection was added to PyWolf's graphical user interface (GUI), enabling users to select the propagation medium of interest. It also enables input parameters (e.g., refractive index) for each propagation model. PyWolf checks for the Python scripts present in the “propagation models” folder at startup and displays them in the GUI, similar to what is done, for instance, for the source models. Then, during the simulation, instead of using the same free space propagators, PyWolf will use the ones that are defined in the selected propagation model. Four examples of propagation models are present in the current version, namely, free space, constant refractive index (besides 1), Kolmogorov, and Tatarskii models [2,3]. Depending on the model used, some propagation quantities may not be valid. For instance, in the current implementation for free space propagation, both the spectral density and degree of coherence are valid, however, that is not the case for the current implementations of the Kolmogorov and Tatarskii models, where only the spectral density is valid. Besides this main feature added to PyWolf, other small issues have been improved and corrected, namely: (i) PyWolf now initiates without needing PyOpenCl platforms or devices; (ii) some errors associated with the importation of packages have been corrected; and (iii) phase correction in the FFT algorithm for odd arrays which can affect the propagation image.Nature of problem: Numerical simulations of the propagation of partially coherent light from planar sources in the Fresnel or far field approximations. Computation time can be improved by using optimized versions of the fast Fourier transform algorithm, but the computation time of other tasks can also be improved through parallel computation. PyWolf aims at using parallel computation to perform time-consuming calculations in the propagation of the cross-spectral density function [4,5].Solution method: The open-source toolkit PyOpenCL is used to perform parallel computation on time-consuming calculations. The user can easily modify and add more features to the software, such as source and propagation models. A graphical user interface is also built using PyQt5 which enables the user to set input parameters, including the user's custom models, view the simulation results, export data, and save and load sessions.

No sign problem in one-dimensional path integral Monte Carlo simulation of fermions: A topological proof.

This paper shows that, in one dimension, due to its topology, a closed-loop product of short-time propagators is always positive, despite the fact that each antisymmetric free fermion propagator can be of either sign.

A correspondence between the free and interacting field

We discover a correspondence between the free field and the interacting states. This correspondence is firstly given from the fact that the free propagator can be converted into a tower of propagators for massive states, when expanded with the Hermite function basis. The equivalence of propagators reveals that in this particular case the duality can naturally be regarded as the equivalence of one theory on the plane wave basis to the other on the Hermite function basis. More generally, the Hermite function basis provides an alternative quantization process with the creation/annihilation operators that correspond directly to the interacting fields. As an illustration, we apply this basis to the 3+1 dimensional Yang–Mills theory, where the three-dimensional space being reduced through the Hermite function basis, and an auxiliary parameter omega denotes for string tension. At large omega limit, with then considering only the lowest order Hermite function (Lowest Landau Level), the equivalent action becomes the Banks–Fischler–Shenker–Susskind (BFSS) matrix model. At small omega limit, the perturbative series summed over all orders of Hermite function gives a massive gluon propagator.

Higher-Spin Currents, Operator Mixing and UV Asymptotics in Large-N QCD-like Theories

We extend to operator mixing—specifically, to higher-spin twist-2 operators—the asymptotic theorem on the ultraviolet asymptotics of the spectral representation of 2-point correlators of multiplicatively renormalizable operators in large-N confining QCD-like theories. The extension is based on a recent differential geometric approach to operator mixing that involves the Poincaré-Dulac theorem and allows us to reduce generically the operator mixing to the multiplicatively renormalizable case, provided that γ0β0 is diagonalizable and a certain nonresonant condition for its eigenvalues holds according to the Poincaré-Dulac theorem, with γ0 and β0 the one-loop coefficients of the anomalous dimension matrix and beta function respectively. Relatedly, we solve a conundrum about the generic nonconservation of higher-spin currents versus the conservation—up to contact terms—of the corresponding free propagators in the spectral representation of 2-point correlators of higher-spin operators of pure integer spin to the leading large-N order.

Sextic tensor model in rank 3 at next-to-leading order

We compute the four-loop beta functions of short and long-range multi-scalar models with general sextic interactions and complex fields. We then specialize the beta functions to a U(N)3 symmetry and study the renormalization group at next-to-leading order in N and small ϵ. In the short-range case, ϵ is the deviation from the critical dimension while it is the deviation from the critical scaling of the free propagator in the long-range case. This allows us to find the 1/N corrections to the rank-3 sextic tensor model of [1]. In the short-range case, we still find a non-trivial real IR stable fixed point, with a diagonalizable stability matrix. All couplings, except for the so-called wheel coupling, have terms of order ϵ0 at leading and next-to-leading order, which makes this fixed point different from the other melonic fixed points found in quartic models. In the long-range case, the corrections to the fixed point are instead not perturbative in ϵ and hence unreliable; we thus find no precursor of the large-N fixed point.

A consistent approach to the path integral formalism of quantum mechanics based on the maximum length uncertainty

We have developed a proper path integral formalism consistent with the deformed version of the quantum mechanics that contains a maximum observable length scale at the order of the cosmological particle horizon, existing in cosmology. We have started by modifying the classical mechanics which shows non-minimal effects on the equation of motion of a particle. Next, we have provided representation of the deformed quantum mechanical algebra. With this algebra in hand, we have calculated the general form of the path integral propagator in this deformed background. Thereafter, as a most simple case, we have built up the explicit form of the free particle propagator. The modifications to the free particle propagator show some non-trivial effects in this case. Our formalism can be applied to analyze the quantum properties and observations emerging in the context of cosmology.

Path Integral Action for a Resonant Detector of Gravitational Waves in the Generalized Uncertainty Principle Framework

The Heisenberg uncertainty principle is modified by the introduction of an observer-independent minimal length. In this work, we have considered the resonant gravitational wave detector in the modified uncertainty principle framework, where we have used the position momentum uncertainty relation with a quadratic order correction only. We have then used the path integral approach to calculate an action for the bar detector in the presence of a gravitational wave and then derived the Lagrangian of the system, leading to the equation of motion for the configuration-space position coordinate in one dimension. We then find a perturbative solution for the coordinate of the detector for a circularly polarized gravitational wave, leading to a classical solution of the same for the given initial conditions. Using this classical form of the coordinate of the detector, we finally obtain the classical form of the on-shell action describing the harmonic oscillator–gravitational wave system. Finally, we have obtained the free particle propagator containing the quantum fluctuation term considering gravitational wave interaction.

Partially massless theory as a quantum gravity candidate

We study partially massless gravity theory (PM gravity theory) and suggest an alternative way to add higher order interaction vertices to the theory. Rather than introducing self-interaction vertices of the gravitational fields to the partially massless gravity action, we consider interactions with matter fields, since it is well known that addition of the self-interaction terms necessarily breaks the [Formula: see text] gauge symmetry that PM gravity theory enjoys. For the coupling with matter fields, we consider two different types of interaction vertices. The first one is given by an interaction Lagrangian density, [Formula: see text], where [Formula: see text] is the PM gravity field and [Formula: see text] is the stress-energy tensor of the matter fields. To retain the [Formula: see text] gauge symmetry, the matter fields also transform accordingly and it turns out that the transform must be nonlocal in this case. The second type of interaction is obtained by employing a gauge covariant derivative with the PM gravity field, where the PM gravity fields play a role of a gauge connection canceling the phase shift of the matter fields. We also study the actions and the equations of motion of the partially massless gravity fields. As expected, it shows 4 unitary degrees of freedom — 2 of them are traceless tensor modes and they are light-like fields and the other 2 are transverse vector modes and their dispersion relation changes as background space–time (de Sitter) evolutes. In the very early time, they are light-like but in the very late time, their velocities become a half of speed of light. The vector mode dispersion relation shows momentum-dependent behavior. In fact, the higher (lower) frequency modes show the faster (slower) velocity. We call this effect “conformal (or de Sitter) prism”. We suggest their quantization, compute Hamiltonians to present their exited quanta and construct their free propagators.

Lattice Landau gauge photon propagator for 4D compact QED

In this work we report on the Landau gauge photon propagator computed for pure gauge 4D compact QED in the confined and deconfined phases and for large lattices volumes: $32^4$, $48^4$ and $96^4$. In the confined phase, compact QED develops mass scales that render the propagator finite at all momentum scales and no volume dependence is observed for the simulations performed. Furthermore, for the confined phase the propagator is compatible with a Yukawa massive type functional form. For the deconfined phase the photon propagator seems to approach a free field propagator as the lattice volume is increased. In both cases, we also investigate the static potential and the average value of the number of Dirac strings in the gauge configurations $m$. In the confined phase the mass gap translates into a linearly growing static potential, while in the deconfined phase the static potential approaches a constant at large separations. Results shows that $m$ is, at least, one order of magnitude larger in the confined phase and confirm that the appearance of a confined phase is connected with the topology of the gauge group.

Cross Section for Bhabha and Compton Scattering Beyond Quantum Field Theory

We consider the theory of spinor fields written in polar form, that is the form in which the spinor components are given in terms of a module times a complex unitary phase respecting Lorentz covariance. In this formalism, spinors can be treated in their most general mathematical form, without the need to restrict them to plane waves. As a consequence, calculations of scattering amplitudes can be performed by employing the most general fermion propagator, and not only the free propagator usually employed in QFT. In this article, we use these quantities to perform calculations in two notable processes, the electron-positron and Compton scatterings. We show that although the methodology differs from the one used in QFT, the final results in the two examples turn out to give no correction as predicted by QFT.

Noncommutativity of the static and homogeneous limit of the axial chemical potential in the chiral magnetic effect

We study the noncommutativity of different orders of zero energy-momentum limit pertaining to the axial chemical potential in the chiral magnetic effect. While this noncommutativity issue originates from the pinching singularity at one-loop order, it cannot be removed by introducing a damping term to the fermion propagators. The physical reason is that modifying the propagator alone would violate the axial-vector Ward identity and as a result a modification of the longitudinal component of the axial-vector vertex is required, which contributes to chiral magnetic effect (CME). The pinching singularity with free fermion propagators was then taken over by the singularity stemming from the dressed axial-vector vertex. We show this mechanism by a concrete example. Moreover, we proved, in general, the vanishing CME in the limit order that the static limit was taken prior to the homogeneous limit in the light of Coleman-Hill theorem for a static external magnetic field. For the opposite limit that the homogeneous limit is taken first, we show that the nonvanishing CME was a consequence of the nonrenormalization of chiral anomaly for an arbitrary external magnetic field.

Trifundamental quartic model

We consider a multi-scalar field theory with either short-range or long-range free action and with quartic interactions that are invariant under $O(N_1)\times O(N_2) \times O(N_3)$ transformations, of which the scalar fields form a tri-fundamental representation. We study the renormalization group fixed points at two loops at finite $N$ and in various large-$N$ scaling limits for small $\epsilon$, the latter being either the deviation from the critical dimension or from the critical scaling of the free propagator. In particular, for the homogeneous case $N_i = N$ for $i=1,2,3$, we study the subleading corrections to previously known fixed points. In the short-range model, for $\epsilon N^2\gg 1$, we find complex fixed points with non-zero tetrahedral coupling, that at leading order reproduce the results of arXiv:1707.03866 ; the main novelty at next-to-leading order is that the critical exponents acquire a real part, thus allowing a correct identification of some fixed points as IR stable. In the long-range model, for $\epsilon N \ll 1 $, we find again complex fixed points with non-zero tetrahedral coupling, that at leading order reproduce the line of stable fixed points of arXiv:1903.03578; at next-to-leading order, this is reduced to a discrete set of stable fixed points. One difference between the short-range and long-range cases is that, in the former the critical exponents are purely imaginary at leading-order and gain a real part at next-to-leading order, while for the latter the situation is reversed.

Space-time-resolved quantum electrodynamics description of Compton scattering

The standard method for approaching quantum electrodynamic (QED) field theory uses a perturbative $S$-matrix approach. This approach is explicitly nondynamical and provides only a one-time, static map between an initial state to be evolved by the ``full propagator'' of a bona-fide interacting field theory and an asymptotically equivalent effective initial state to be evolved by the ``free propagator'' of the corresponding noninteracting field theory. We provide a detailed derivation of a nonperturbative and dynamical approach to QED that allows one to study the space-time dynamics of electron-photon interactions directly. As an example of this method, we compute the time-resolved dynamics of Compton scattering for a system with a nontrivial spatial structure in only one dimension while restricting to the case of a single electron and at most one photon. This approach retains the massless photon of quantum electrodynamics in contrast to previous approaches that resorted to using massive bosons [T. Cheng, E. R. Gospodarczyk, Q. Su, and R. Grobe, Ann. Phys. 325, 265 (2010)] to represent the photon. The dynamics of Compton scattering are illustrated using joint probability distributions that evolve in time. This information is compared to that provided by the $S$ matrix.

Free fall in KvN mechanics and Einstein’s principle of equivalence

The implementation of Einstein’s principle of equivalence in Koopman–von Neumann (KvN) mechanics is discussed. The implementation is very similar to the implementation of this principle in quantum mechanics. This is not surprising, because KvN mechanics provides a Hilbert space formulation of classical mechanics that is very similar to the quantum mechanical formalism.Both in KvN mechanics and quantum mechanics, a propagator in a homogeneous gravitational field is simply related with a free propagator. As a result, the wave function in a homogeneous gravitational field in a freely falling reference frame differs from the free wave function only in phase.Fisher information, which quantifies our ability to estimate mass from coordinate measurements, does not depend on the magnitude of the homogeneous gravitational field, and this fact constitutes the formulation of Einstein’s principle of equivalence, which is valid both in quantum mechanics and KvN mechanics.

Sextic tensor field theories in rank 3 and 5

We study bosonic tensor field theories with sextic interactions in d < 3 dimensions. We consider two models, with rank-3 and rank-5 tensors, and U(N)3 and O(N)5 symmetry, respectively. For both of them we consider two variations: one with standard short-range free propagator, and one with critical long-range propagator, such that the sextic interactions are marginal in any d < 3. We derive the set of beta functions at large N , compute them explicitly at four loops, and identify the respective fixed points. We find that only the rank-3 models admit melonic interacting fixed points, with real couplings and critical exponents: for the short-range model, we have a Wilson-Fisher fixed point with couplings of order sqrt{epsilon } , in d = 3 − ϵ; for the long-range model, instead we have for any d < 3 a line of fixed points, parametrized by a real coupling g1 (associated to the so-called wheel interaction). By standard conformal field theory methods, we then study the spectrum of bilinear operators associated to such interacting fixed points, and we find a real spectrum for small ϵ or small g1.