Quantum Field Theory Research Articles

Phonon-photon conversion as mechanism for cooling and coherence transfer

The dynamical Casimir effect is the physical phenomenon where the mechanical energy of a movable wall of a cavity confining a quantum field can be converted into quanta of the field itself. This effect has been recognized as one of the most astonishing predictions of quantum field theory. At the quantum scale, the energy conversion can also occur incoherently, namely, without a physical motion of the wall. By means of quantum thermodynamics, we show that this phenomenon can be employed as a tool to cool down the wall when there is a nonvanishing temperature gradient between the wall and the cavity. At the same time, the mechanism responsible for the heat transfer enables sharing the coherence from one cavity mode, driven by a laser, to the wall, thereby forcing its coherent oscillation. Finally, we show how to employ one laser drive to cool the entire system, including the case when it is composed of other subsystems. Published by the American Physical Society 2024

Worldline approach for spinor fields in manifolds with boundaries

The worldline formalism is a useful scheme in Quantum Field Theory which has also become a powerful tool for numerical computations. It is based on the first quantisation of a point-particle whose transition amplitudes correspond to the heat-kernel of the operator of quantum fluctuations of the field theory. However, to study a quantum field theory in a bounded manifold one needs to restrict the path integration domain of the point-particle to a specific subset of worldlines enclosed by those boundaries. In the present article it is shown how to implement this restriction for the case of a spinor field in a two-dimensional curved half-plane under MIT bag boundary conditions, and compute the first few heat-kernel coefficients as a verification of the proposed construction. This construction admits several generalisations.

Practical derivations of fermion and gauge boson reduction formulae in curved spacetimes

LSZ-type reduction formulae are derived for gauge fields and fermions in curved spacetime. The formulae are derived using a conserved current method applicable also to flat spacetimes. The method generalizes to more general quantum field theories. The formulae are then applied to a couple of basic problems to illustrate their use.

Path integrals, complex probabilities and the discrete Weyl representation

A discrete formulation of the real-time path integral as the expectation value of a functional of paths with respect to a complex probability on a sample space of discrete valued paths is explored. The formulation in terms of complex probabilities is motivated by a recent reinterpretation of the real-time path integral as the expectation value of a potential functional with respect to a complex probability distribution on cylinder sets of paths. The discrete formulation in this work is based on a discrete version of the Weyl algebra that can be applied to any observable with a finite number of outcomes. The origin of the complex probability in this work is the completeness relation. In the discrete formulation the complex probability exactly factors into products of conditional probabilities and exact unitarity is maintained at each level of approximation. The approximation of infinite dimensional quantum systems by discrete systems is discussed. The method is illustrated by applying it to scattering theory and quantum field theory. The implications of these applications for quantum computing is discussed.

Alternative to perturbative renormalization in ( 3+1 )-dimensional field theories

Perturbative renormalization provides the bedrock of understanding quantum field theories. In this work, I point out an alternative way of renormalizing quantum field theories, which is naturally encountered and well-known for the case of large N scalar field theories. In terms of bare parameters, this nonperturbative alternative renormalization differs qualitatively from its perturbative cousin: in the continuum limit, the bare coupling constant goes to zero instead of infinity, and there is no wave-function counterterm. Despite these differences, the resulting n-point functions of the theory are finite. I provide explicit results for alternative renormalization for the O(N) model and QCD with Nf=12 flavors in 3+1 dimensions. Published by the American Physical Society 2024

Evolution of strictly localized states in noninteracting quantum field theories with background fields

Evolution of strictly localized states in noninteracting quantum field theories with background fields

Tangleoids with quantum field theories in biosystems

Abstract The open question whether quantum field theories can be used in biological systems will be addressed in this study. Quantum effects were reported for certain biological systems like the magnetic orientation sense in migratory birds. In quantum field theories it is possible to derive effective quantum field theories with welded tangleoids including braid relations that describe composite particles based on the dynamics of microscopic particle where these composite particles are made of. We observe that the generators of the tangleoid category that will depict the Feynman graphs are X X for a scattering vertex. This arises after carrying out the integral over bosonic fields A μ {A}_{\mu } in the partition function (D) that will lead to an four-valent interaction vertex generated by a quartic term in the fermionic fields. With X + {X}_{+} and X − {X}_{-} we will depict order changes like that regarding time orderings. Ordinary propagators are depicted by ∪ \cup and ∩ \cap . Finally, the generators ! \! and ¡ \hspace{0.1em}\text{¡}\hspace{0.1em} come into play if other foreign fields are picked up.

Tropological sigma models

With the use of mathematical techniques of tropical geometry, it was shown by Mikhalkin some twenty years ago that certain Gromov-Witten invariants associated with topological quantum field theories of pseudoholomorphic maps can be computed by going to the tropical limit of the geometries in question. Here we examine this phenomenon from the physics perspective of topological quantum field theory in the path integral representation, beginning with the case of the topological sigma model before coupling it to topological gravity. We identify the tropicalization of the localization equations, investigate its geometry and symmetries, and study the theory and its observables using the standard cohomological BRST methods. We find that the worldsheet theory exhibits a nonrelativistic structure, similar to theories of the Lifshitz type. Its path-integral formulation does not require a worldsheet complex structure; instead, it is based on a worldsheet foliation structure.

The Schmidt Rank for the Commuting Operator Framework

In quantum information theory, the Schmidt rank is a fundamental measure for the entanglement dimension of a pure bipartite state. Its natural definition uses the Schmidt decomposition of vectors on bipartite Hilbert spaces, which does not exist (or at least is not canonically given) if the observable algebras of the local systems are allowed to be general C*-algebras. In this work, we generalize the Schmidt rank to the commuting operator framework where the joint system is not necessarily described by the minimal tensor product but by a general bipartite algebra. We give algebraic and operational definitions for the Schmidt rank and show their equivalence. We analyze bipartite states and compute the Schmidt rank in several examples: the vacuum in quantum field theory, Araki–Woods-Powers states, as well as ground states and translation invariant states on spin chains which are viewed as bipartite systems for the left and right half chains. We conclude with a list of open problems for the commuting operator framework.

McGinty-Nottale Scale Equation (MNSE): A Paradigm Shift in Quantum Mechanics

In the dynamic realm of theoretical physics, the quest to unify and reconcile distinct theories often catalyzes groundbreaking advancements. This paper introduces the MNSE, an innovative theoretical framework that synergizes the McGinty Equation (MEQ) with Laurent Nottale’s Scale Relativity. The MEQ, notable for its incorporation of fractal geometry into Quantum Field Theory (QFT), intersects with Scale Relativity’s premise of space-time’s fractal structure and scale-dependent physical laws. The resultant MNSE posits a profound transformation in our comprehension of quantum mechanics, offering a nuanced perspective on the intricate nature of space-time and quantum phenomena. This paper aims to dissect the complexities of this integration, illuminating how the MNSE redefines our understanding of quantum communication, and delineates its vast implications for global connectivity and information security.

A Quantization for the Toy Model of Black Hole and a Suggestion to the Unification Theory

In my previous paper about the correlations about the quantum mechanics between four different natural forces, I have suggested that there may be a fifth force or even the existence of a new particle. However, it may be still a mysterious that physicists for nearly hundreds of years that they cannot unify these four natural forces. This may be because there are indeed too many variables for them considerate. Also there is a twin such that the quantum machanics may coexist with the quantum field theory. In the present paper, this author proposes that there may be a misconcept in the computational equation for our relative time or the gaps in the system of measure time between quantum mechanics and general relativity. Hence, one may still cannot unify these natural forces. This author suggests that we need to rewrite parts of our QM – the Schrödinger Equation or even the GR equation. Besides, this author also proposes there may be a bridge converting equation for the quantum mechanics and the general relativity. Moreover, this author has employed the non-trivial zeta zeros to stimulate the black hole or the so-called black hole toy model. In practice, there may be an electromagnetic field laying around the boundary of the black hole as well as the existing of a continumm in the such boundary contour. This author hopes that in such case, we may decode back those high frequency electromagnetic waves into the useful information and may go a further step to have a verification for the famous Stephen Hawking’s theory between the black hole radition and the information entropy. In fact, this author has used the HKLam statistical model theory to express the electromagnetic field energy-stress tensor (with the possibility of quantization) to analogically establish a quantized model for the Einstein Gravitational Field Equation. Hence, the problem of the quantum gravity may then be solved. Last but not least, this author may also expect that we – human may finally find a way to unify the quantum mechanics and the general relativity through the modification to the present quantum gravity theory from my suggested bridge converting equation etc.

Completing the bootstrap program for TT― -deformed massive integrable quantum field theories

In recent years a considerable amount of attention has been devoted to the investigation of 2D quantum field theories perturbed by certain types of irrelevant operators. These are the composite field TT― —constructed out of the components of the stress-energy tensor—and its generalisations—built from higher-spin conserved currents. The effect of such perturbations on the infrared and ultraviolet properties of the theory has been extensively investigated. In the context of integrable quantum field theories, a fruitful perspective is that of factorised scattering theory. In fact, the above perturbations were shown to preserve integrability. The resulting deformed scattering matrices—extensively analysed with the thermodynamic Bethe ansatz—provide the first step in the development of a bootstrap program. In this paper we present a systematic approach to computing matrix elements of operators in generalised TT― -perturbed models, based on employing the standard form factor program. We show that for theories with diagonal scattering and certain types of fields the deformed form factors, factorise into the product of the undeformed ones and of a perturbation- and theory-dependent term. From these solutions, correlation functions can be obtained and their asymptotic properties studied.

Bundle Structure of Massless Unitary Representations of the Poincaré Group

Reviewing the construction of induced representations of the Poincaré group of four-dimensional spacetime we find all massive representations, including the ones on interacting many-particle states. Massless momentum wavefunctions of non-vanishing helicity turn out to be more precisely sections of a U(1)-bundle over the massless shell, a property which to date was overlooked in quantum field theory and in bracket notation. Our traditional notation of states in Hilbert space enables questions about square integrability and smoothness. Their answers complete the picture of relativistic quantum physics. Frobenius reciprocity prohibits massless one-particle states with total angular momentum less than the modulus of the helicity. There is no two-photon state with J=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J=1$$\\end{document}, explaining the longevity of orthopositronium. Partial derivatives of the momentum wave functions are no operators in the space of massless states with nonvanishing helicity. They allow only for covariant, noncommuting derivatives. The massless shell has a noncommutative geometry with helicity being its topological charge.

Non-polynomial interactions as a path towards a non-renormalizable UV-completion

We propose a new class of single-field scalar quantum field theories with non-polynomial interactions leading to a two-point Green's function that can be naturally continued beyond the naive cutoff scale. This provides a new prospect for self-completing theories in the UV-domain. In our approach, the formal power series for the scalar potential has a vanishing radius of convergence and is defined through Borel resummation. We discuss concrete examples, among others with a spectral function that vanishes at large momenta, potentially leading to an asymptotically free theory. Finally, we give an outlook on future research, with a view towards possible applications to inflation and gravity.

Conservative Black Hole Scattering at Fifth Post-Minkowskian and First Self-Force Order

We compute the fifth post-Minkowskian (5PM) order contributions to the scattering angle and impulse of classical black hole scattering in the conservative sector at first self-force order using the worldline quantum field theory formalism. This challenging four-loop computation required the use of advanced integration-by-parts and differential equation technology implemented on high-performance computing systems. Use of partial fraction identities allowed us to render the complete integrand in a fully planar form. The resulting function space is simpler than expected: In the scattering angle, we see only multiple polylogarithms up to weight three and a total absence of the elliptic integrals that appeared at 4PM order. All checks on our result, both internal—cancellation of dimensional regularization poles and preservation of the on-shell condition—and external—matching the slow-velocity limit with the post-Newtonian (PN) literature up to 5PN order and matching the tail terms to the 4PM loss of energy—are passed. Published by the American Physical Society 2024

Krylov complexity in quantum field theory, and beyond

We study Krylov complexity in various models of quantum field theory: free massive bosons and fermions on flat space and on spheres, holographic models, and lattice models with a UV-cutoff. In certain cases, we observe asymptotic behavior in Lanczos coefficients that extends beyond the previously observed universality. We confirm that, in all cases, the exponential growth of Krylov complexity satisfies the conjectured inequality, which generalizes the Maldacena-Shenker-Stanford bound on chaos. We discuss the temperature dependence of Lanczos coefficients and note that the relationship between the growth of Lanczos coefficients and chaos may only hold for the sufficiently late, truly asymptotic regime, governed by physics at the UV cutoff. Contrary to previous suggestions, we demonstrate scenarios in which Krylov complexity in quantum field theory behaves qualitatively differently from holographic complexity.

Once upon a time in superspace: the diegetic ideal for the interpretation of physical theories

This paper offers a novel argument for superspace substantivalism. Superspace is a modified spacetime represented formally through combining ordinary spatial dimensions with anticommuting dimensions whose coordinates are labelled in Grassmann numbers rather than real numbers. At supersymmetric worlds, physical laws exhibit supersymmetry—viz., a symmetry that transforms bosons into fermions and vice versa. Superspace substantivalism is the thesis that, at supersymmetric worlds, among the most fundamental structures is superspace. Initially, the focus will be on a prevalent doctrine in the philosophy of physics literature which I call the mimetic ideal. On the mimetic ideal, interpreting physical theories aims primarily at specifying their ontology, namely at achieving accurate reference (in natural-language accounts of those theories) or representation (in model-theoretic portrayals of those theories) with respect to aspects of physical reality. However, I show that the mimetic ideal doesn’t seem able to account for important aspects of physics practice (Sect. 2). In Sect. 3, therefore, I articulate and defend a new, diegetic ideal, according to which the interpretation of physical theories should aim at perspectival coordination between interpreters and practising physicists. Perspectival coordination, in the context of interpreting physical theories, means that interpreters and practising physicists share a perspective or a point of view on some aspect of physical reality described by that theory. In Sect. 4, I apply this analysis to the study of supersymmetric quantum field theories (QFTs): reframing the realist framework which underlies Baker’s (2020) agnosticism, I examine the exciting upshot that superspace substantivalism is true. I conclude with some reflections on what perspectival coordination means for realism (Sect. 5).

A holographic entanglement entropy at spi

Defining finite entanglement entropy for a subregion in quantum field theory requires the introduction of two logically independent scales: an IR scale that controls the size of the subregion, and a UV cut-off. In AdS/CFT, the IR scale is the AdS lengthscale, the UV cut-off is the bulk radial cut-off, and the subregion is specified by dimensionless angles. This is the data that determines Ryu-Takayanagi surfaces and their areas in AdS/CFT. We argue that in asymptotically flat space there exists the notion of a “spi-subregion” that one can associate to spatial infinity (spi). Even though geometrically quite different from an AdS subregion, this angle data has the crucial feature that it allows an interpretation as a bi-partitioning of spi. Therefore, the area of the RT surface associated to the spi-subregion can be interpreted as the entanglement entropy of the reduced density matrix of the bulk state under this bi-partition, as in AdS/CFT. For symmetric spi-subregions, these RT surfaces are the waists of Asymptotic Causal Diamonds. In empty flat space they reduce to Rindler horizons, and are analogues of the AdS-Rindler horizons of Casini, Huerta & Myers. We connect these results to previous work on minimal surfaces anchored to screens in empty space, but also generalize the discussion to the case where there are black holes in the bulk. The phases of black hole RT surfaces as the spi-subregion is varied, naturally connect with those of black holes (small and large) in AdS. A key observation is that the radial cut-off is associated to an IR scale in flat space — and in fact there are no UV divergences. We argue that this is consistent with previous suggestions that in sub-AdS scales the holographic duality is an IR/IR correspondence and that the degrees of freedom are not those of a local QFT, but those of long strings. Strings are of course, famously UV finite.

Remarks on quantum mechanics and non-reflexive logic

In this paper we discuss and outline a version of non-relativistic quantum mechanics based on a new non-reflexive logic, where the basic entities (elementary particles) lack identity conditions. Some relationships with quantum field theories are also sketched.

Electric-magnetic duality and Z2 symmetry enriched Abelian lattice gauge theory

Kitaev’s quantum double model is a lattice realization of Dijkgraaf–Witten topological quantum field theory. Its topologically protected ground state space has broad applications for topological quantum computation and topological quantum memory. We investigate the Z2 symmetry enriched generalization of the model for the Abelian group in a categorical framework and present an explicit Hamiltonian construction. This model provides a lattice realization of the Z2 symmetry of the topological phase. We discuss in detail the categorical symmetry of the phase, for which the electric-magnetic (EM) duality symmetry is a special case. The aspects of symmetry defects are investigated using the G-crossed unitary braided fusion category. By determining the corresponding anyon condensation, the gapped boundaries and boundary-bulk duality are also investigated. In the last part, an explicit lattice realization of EM duality is discussed.