Non-relativistic Quantum Field Theory Research Articles

Quantum vacuum effects in nonrelativistic quantum field theory

Quantum vacuum effects in nonrelativistic quantum field theory

Variational Neural-Network Ansatz for Continuum Quantum Field Theory.

Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In nonrelativistic quantum field theories, the challenge is to parametrize and optimize over the infinitely many n-particle wave functions comprising the state's Fock-space representation. Here we approach this problem by introducing neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to nonrelativistic quantum field theories in the continuum. Our ansatz uses the Deep Sets neural network architecture to simultaneously parametrize all of the n-particle wave functions comprising a quantum field state. We employ our ansatz to approximate ground states of various field theories, including an inhomogeneous system and a system with long-range interactions, thus demonstrating a powerful new tool for probing quantum field theories.

Multipolar quantum electrodynamics of localized charge-current distributions: Spectral theory and renormalization

We formulate a nonrelativistic quantum field theory to model interactions between quantized electromagnetic fields and localized charge-current distributions. The electronic degrees of freedom are encoded in microscopic polarization and magnetization field operators whose moments are identified with the multipole moments of the charge-current distribution. The multipolar Hamiltonian is obtained from the minimal coupling Hamiltonian through a unitary transformation, often referred to as the Power-Zienau-Woolley transformation; we renormalize this Hamiltonian using perturbation theory, the result of which is used to compute the leading-order radiative corrections to the electronic energy levels due to interactions between the electrons and quantum vacuum fluctuations in the electromagnetic field. Our renormalized energy shift constitutes a generalization of the Lamb shift in atomic hydrogen, valid for general localized assemblies of atoms and molecules, possibly with net charge but absent a free current. By expanding the fields in a series of multipole moments, our results can be used to study contributions to this energy shift coming from specific multipole moments of arbitrary order.

Hamiltonians for Polaron Models with Subcritical Ultraviolet Singularities

We treat the ultraviolet problem for polaron-type models in nonrelativistic quantum field theory. Assuming that the dispersion relations of particles and the field have the same growth at infinity, we cover all subcritical (superrenormalisable) interactions. The Hamiltonian without cutoff is exhibited as an explicit self-adjoint operator obtained by a finite iteration procedure. The cutoff Hamiltonians converge to this operator in the strong resolvent sense after subtraction of a perturbative approximation for the ground-state energy.

Spatial entanglement in interacting Bose-Einstein condensates

The entanglement between spatial regions in an interacting Bose-Einstein condensate is investigated using a quantum field theoretic formalism. Regions that are small compared to the healing length are governed by a non-relativistic quantum field theory in the vacuum limit, and we show that the latter has vanishing entanglement. In the opposite limit of a region that is large compared to the healing length, the entanglement entropy is like in the vacuum of a relativistic theory where the velocity of light is replaced with the velocity of sound and where the inverse healing length provides a natural ultraviolet regularization scale. Besides the von Neumann entanglement entropy, we also calculate R\'enyi entanglement entropies for a one-dimensional quasi-condensate.

Geometrizing non-relativistic bilinear deformations

We define three fundamental solvable bilinear deformations for any massive non-relativistic 2d quantum field theory (QFT). They include the mathrm{T}overline{mathrm{T}} deformation and the recently introduced hard rod deformation. We show that all three deformations can be interpreted as coupling the non-relativistic QFT to a specific Newton-Cartan geometry, similar to the Jackiw-Teitelboim-like gravity in the relativistic case. Using the gravity formulations, we derive closed-form deformed classical Lagrangians of the Schrödinger model with a generic potential. We also extend the dynamical change of coordinate interpretation to the non-relativistic case for all three deformations. The dynamical coordinates are then used to derive the deformed classical Lagrangians and deformed quantum S-matrices.

Quantum superposition of two gravitational cat states

We extend our earlier work [] on probing a gravitational cat state (gravcat) to the quantum superposition of two gravcats in an exemplary model and in Bose–Einstein condensates (BEC). In addition to its basic theoretical values in gravitational quantum physics and macroscopic quantum phenomena, this investigation can provide some theoretical support to experimental proposals for measuring gravity-induced entanglement and the quantum nature of perturbative gravity. In the first part we consider cat states generated by double-well potentials. A pair of gravcats, each approximated as a two-level system, is characterized by gravity-induced Rabi oscillations, and by gravity-induced entanglement of its energy eigenstates. In the second part we turn to a (non-relativistic) quantum field theory description and derive a gravitational Gross–Pitaevsky equation for gravcats formed in BEC. Using a mathematical analogy to quantum rotors, we explore the properties of the two-gravcat system for BECs, its physical consequences and observational possibilities. Finally we discuss our results in comparison to predictions of alternative quantum theories, and we explain their implications.

The Entropic Dynamics of Quantum Scalar Fields Coupled to Gravity

Entropic dynamics (ED) are a general framework for constructing indeterministic dynamical models based on entropic methods. ED have been used to derive or reconstruct both non-relativistic quantum mechanics and quantum field theory in curved space-time. Here we propose a model for a quantum scalar field propagating in dynamical space-time. The approach rests on a few key ingredients: (1) Rather than modelling the dynamics of the fields, ED models the dynamics of their probabilities. (2) In accordance with the standard entropic methods of inference, the dynamics are dictated by information encoded in constraints. (3) The choice of the physically relevant constraints is dictated by principles of symmetry and invariance. The first of such principle imposes the preservation of a symplectic structure which leads to a Hamiltonian formalism with its attendant Poisson brackets and action principle. The second symmetry principle is foliation invariance, which, following earlier work by Hojman, Kuchař, and Teitelboim, is implemented as a requirement of path independence. The result is a hybrid ED model that approaches quantum field theory in one limit and classical general relativity in another, but is not fully described by either. A particularly significant prediction of this ED model is that the coupling of quantum fields to gravity implies violations of the quantum superposition principle.

Different instances of time as different quantum modes: quantum states across space-time for continuous variables

Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in general relativity space-time is taken as a combinator, curved around mass. Here we present a unified approach on both space and time in quantum theory, and build quantum states across spacetime instead of only on spatial slices. We no longer distinguish measurements on the same system at different times with measurements on different systems at one time and construct spacetime states upon these measurement statistics. As a first step towards non-relativistic quantum field theory, we consider how to approach this in the continuous-variable multi-mode regime. We propose six possible definitions for spacetime states in continuous variables, based on four different measurement processes: quadratures, displaced parity operators, position measurements and weak measurements. The basic idea is to treat different instances of time as different quantum modes. They are motivated by the pseudo-density matrix formulation among indefinite causal structures and the path integral formalism. We show that these definitions lead to desirable properties, and raise the differences and similarities between spatial and temporal correlations. An experimental proposal for tomography is presented, construing the operational meaning of the spacetime states.

Quantization of Newton’s Gravity

In this work we will use a recently developed non relativistic (NR) quantization methodology that successfully overcomes troubles with infinities that plague non-renormalizable quantum field theories (QFTs). The ensuing methodology is here applied to Newton’s gravitation potential. We employ here the concomitant mathematical apparatus to formulate the NR QFT discussed in the well known classical text-book by Fetter and Walecka. We emphasize the fact that we speak of non relativistic QFT. This is so because we appeal to Newton’s gravitational potential, while in a relativistic QFT one does not employ potentials. Our main protagonist is the notion of propagator. This notion is of the essence in non relativistic quantum field theory (NR-QFT). Indeed, propagators are indispensable tools for both nuclear physics and condensed matter theory, among other disciplines. In the present work we deal with propagators for both fermions and bosons.

Basic Quantum Field Model of the Self-Organization of Microtubules in Eukaryotic Cells

The background of this contribution is the ongoing extended debate over quantum effects in the biology since decades. Typical examples of the quantum biology are photosynthesis, enzymatic activities, bird navigation and especially the coherent movement of microtubules. The reason for all these effects is dominantly the quantum coherence of waves. The objective of this contribution is the quantum description of the instability dynamics of microtubules at their assembly and disassembly phases during the interphase. The corresponding theoretical investigations of this article confirm the existence of quantum coherence of microtubules. Experimental results assert such vibrations of microtubules by the observation of γ-waves in the human brain generated by bundles of microtubules. Tubulin subunits and the accessory proteins are of nano size; therefore, they are modeled as field quanta in the framework of non-relativistic quantum field theory. This approach describes the dynamics of these quantum particles and their interactions, by accentuation of their different performances as coherent or incoherent waves. The achieved results strongly depend from the preconditions: whether the fluctuating forces are turned on or turned off. With the inset of fluctuations, the quantum coherence is destroyed, and only incoherent particle solutions are obeyed. Without the impact of fluctuations wave solutions dominate. Another type of wave solution are coherent wave packets which are counter-running, where their superposition can extinct or enhance them. This kind of interfering coherent solutions is applied on the polymerization of protofilaments. The calculations of this contribution demonstrate that the quantum coherence can be only observed when fluctuations are excluded. The conclusion is that that dedicated biological processes must be able to suppress the destroying influences of the local environment. In contrary to technical-based experiments, where coherence is only obtained when the fluctuations are deliberately excluded (e.g. quantum computer). Therefore, the answer why the processes of quantum biology can generate quantum coherence at least in case of microtubules is actually not answered. Kinesins in combination with microtubules are fundamental for cellular functions and morphogenesis. Recent genetic experiments uncovered their role for tumor suppression and developmental patterning. However, these findings which open exciting new areas of kinesin research are not included in this contribution, because the description of the kinesin-microtubule system is to comprehensive for one article.

Non-relativistic quantum field theory of Verlinde’s emergent entropic gravity

Non relativistic quantum field theory propagators are indispensable tools in nuclear physics and condensed matter theory. Here we apply them to gravitation, that is, discuss a non relativistic quantum field theory for fermions and bosons in a Verlinde-information theory-scenario. In it, gravity becomes an emergent entropic force. In a first previous paper (Plastino and Rocca (2018)), we have shown, via statistical mechanics, that emergent gravity can indeed be thought of as an entropic force at a classical level. In two subsequent works (Plastino and Rocca etal (2019); Plastino and Rocca (2019)) we did the same at a quantum level, for bosons and fermions. Further, the two additional papers (Plastino and Rocca (2019)) discussed the first quantization of EEG for bosons and fermions, by solving the corresponding Schrödinger equations. In the present effort we deal with the pertinent Non-Relativistic (NR) Quantum Field Theory (QFT) corresponding to fermions and bosons’ EEG. With this purpose, we use the results previously obtained in the above mentioned papers together with the formulation of the NR QFT described in the classical text-book by Fetter and Walecka. Note that we are speaking of an NR QFT because we are using Verlinde’s gravitational potential (in relativistic QFT people do not use potentials).

A Nonrelativistic Quantum Field Theory with Point Interactions in Three Dimensions

We construct a Hamiltonian for a quantum-mechanical model of nonrelativistic particles in three dimensions interacting via the creation and annihilation of a second type of nonrelativistic particles, which are bosons. The interaction between the two types of particles is a point interaction concentrated on the points in configuration space where the positions of two different particles coincide. We define the operator, and its domain of self-adjointness, in terms of co-dimension-three boundary conditions on the set of collision configurations relating sectors with different numbers of particles.

Bohmian Trajectories for Hamiltonians with Interior–Boundary Conditions

Recently, there has been progress in developing interior-boundary conditions (IBCs) as a technique of avoiding the problem of ultraviolet divergence in non-relativistic quantum field theories while treating space as a continuum and electrons as point particles. An IBC can be expressed in the particle-position representation of a Fock vector $\psi$ as a condition on the values of $\psi$ on the set of collision configurations, and the corresponding Hamiltonian is defined on a domain of vectors satisfying this condition. We describe here how Bohmian mechanics can be extended to this type of Hamiltonian. In fact, part of the development of IBCs was inspired by the Bohmian picture. Particle creation and annihilation correspond to jumps in configuration space; the annihilation is deterministic and occurs when two particles (of the appropriate species) meet, whereas the creation is stochastic and occurs at a rate dictated by the demand for the equivariance of the $|\psi|^2$ distribution, time reversal symmetry, and the Markov property. The process is closely related to processes known as Bell-type quantum field theories.

Non-relativistic limits and 3D massive gravity

The non-relativistic version of General Relativity, called Newton-Cartan gravity, has received renewed attention as a tool to explore (non-perturbative) properties of non-relativistic quantum field theories. The first part of this talk is a non-specialist introduction to Newton-Cartan geometry; in particular, it is shown how Newton-Cartan gravity arises as a special limit of General Relativity. The second part reviews a novel non-relativistic limit of the 3D massive spin-2 Fierz-Pauli theory to a spin-2 planar Schrodinger equation that has been proposed to describe the so-called GMP gapped spin-2 mode of fractional Quantum Hall states. The talk concludes with speculations on an extension of this non-relativistic limit to interacting massive 3D gravity theories.

Entanglement at a scale and renormalization monotones

We study the information content of the reduced density matrix of a region in quantum field theory that cannot be recovered from its subregion density matrices. We reconstruct the density matrix from its subregions using two approaches: scaling maps and recovery maps. The vacuum of a scale-invariant field theory is the fixed point of both transformations. We define the entanglement of scaling and the entanglement of recovery as measures of entanglement that are intrinsic to the continuum limit. Both measures increase monotonically under the renormalization group flow. This provides a unifying information-theoretic structure underlying the different approaches to the renormalization monotones in various dimensions. Our analysis applies to non-relativistic quantum field theories as well the relativistic ones, however, in relativistic case, the entanglement of scaling can diverge.

Continuous matrix product states for nonrelativistic quantum fields: A lattice algorithm for inhomogeneous systems

By combining the continuous matrix product state (cMPS) representation for quantum fields in the continuum with standard optimization techniques for matrix product states (MPS) on the lattice, we obtain an approximation $|\Psi\rangle$, directly in the continuum, of the ground state of non-relativistic quantum field theories. This construction works both for translation invariant systems and in the more challenging context of inhomogeneous systems, as we demonstrate for an interacting bosonic field in a periodic potential. Given the continuum Hamiltonian $H$, we consider a sequence of discretized Hamiltonians $\{H(\epsilon_{\alpha})\}_{\alpha=1,2,\cdots,p}$ on increasingly finer lattices with lattice spacing $\epsilon_1 > \epsilon_2 > \cdots > \epsilon_p$. We first use energy minimization to optimize an MPS approximation $|\Psi(\epsilon_1)\rangle$ for the ground state of $H(\epsilon_1)$. Given the MPS $|\Psi(\epsilon_{\alpha})\rangle$ optimized for the ground state of $H(\epsilon_{\alpha})$, we use it to initialize the energy minimization for Hamiltonian $H(\epsilon_{\alpha+1})$, resulting in the optimized MPS $|\Psi(\epsilon_{\alpha+1})\rangle$. By iteration we produce an optimized MPS $|\Psi(\epsilon_{p})\rangle$ for the ground state of $H(\epsilon_p)$, from which we finally extract the cMPS approximation $|\Psi\rangle$ for the ground state of $H$. Two key ingredients of our proposal are: (i) a procedure to discretize $H$ into a lattice model where each site contains a two-dimensional vector space (spanned by vacuum $|0\rangle$ and one boson $|1\rangle$ states), and (ii) a procedure to map MPS representations from a coarser lattice to a finer lattice.

Observation of universal dynamics in a spinor Bose gas far from equilibrium.

Predicting the dynamics of quantum systems far from equilibrium represents one of the most challenging problems in theoretical many-body physics1,2. While the evolution of a many-body system is in general intractable in all its details, relevant observables can become insensitive to microscopic system parameters and initial conditions. This is the basis of the phenomenon of universality. Far from equilibrium, universality is identified through the scaling of the spatio-temporal evolution of the system, captured by universal exponents and functions. Theoretically, this has been studied in examples as different as the reheating process in inflationary Universe cosmology3,4, the dynamics of nuclear collision experiments described by quantum chromodynamics5,6, and the post-quench dynamics in dilute quantum gases in non-relativistic quantum field theory7-11. However, an experimental demonstration of such scaling evolution in space and time in a quantum many-body system has been lacking. Here we observe the emergence of universal dynamics by evaluating spatially resolved spin correlations in a quasi-one-dimensional spinor Bose-Einstein condensate12-16. For long evolution times we extract the scaling properties from the spatial correlations of the spin excitations. From this we find the dynamics to be governed by an emergent conserved quantityand the transport of spin excitations towards low momentum scales. Our results establish an important class of non-stationary systems whose dynamics is encoded in time-independent scaling exponents and functions, signalling the existence of non-thermal fixed points10,17,18. We confirm that the non-thermal scaling phenomenon involves no fine-tuningof parameters, by preparing different initial conditions and observing the same scaling behaviour. Our analogue quantum simulation approach provides the basis with which to reveal the underlying mechanisms and characteristics of non-thermal universality classes. One may use this universality to learn, from experiments with ultracold gases, about fundamental aspects of dynamics studied in cosmology and quantum chromodynamics.

Time in Quantum Mechanics and the Local Non-Conservation of the Probability Current

In relativistic quantum field theory with local interactions, charge is locally conserved. This implies local conservation of probability for the Dirac and Klein–Gordon wavefunctions, as special cases; and in turn for non-relativistic quantum field theory and for the Schrödinger and Ginzburg–Landau equations, regarded as low energy limits. Quantum mechanics, however, is wider than quantum field theory, as an effective model of reality. For instance, fractional quantum mechanics and Schrödinger equations with non-local terms have been successfully employed in several applications. The non-locality of these formalisms is strictly related to the problem of time in quantum mechanics. We explicitly compute, for continuum wave packets, the terms of the fractional Schrödinger equation and the non-local Schrödinger equation by Lenzi et al. that break local current conservation. Additionally, we discuss the physical significance of these terms. The results are especially relevant for the electromagnetic coupling of these wavefunctions. A connection with the non-local Gorkov equation for superconductors and their proximity effect is also outlined.

Bootstrapping holographic warped CFTs or: how I learned to stop worrying and tolerate negative norms

We use modular invariance to derive constraints on the spectrum of warped conformal field theories (WCFTs) — nonrelativistic quantum field theories described by a chiral Virasoro and U(1) Kac-Moody algebra. We focus on holographic WCFTs and interpret our results in the simplest holographic set up: three dimensional gravity with Compère-Song-Strominger boundary conditions. Holographic WCFTs feature a negative U(1) level that is responsible for negative norm descendant states. Despite the violation of unitarity we show that the modular bootstrap is still viable provided the (Virasoro-Kac-Moody) primaries carry positive norm. In particular, we show that holographic WCFTs must feature either primary states with negative norm or states with imaginary U(1) charge, the latter of which have a natural holographic interpretation. For large central charge and arbitrary level, we show that the first excited primary state in any WCFT satisfies the Hellerman bound. Moreover, when the level is positive we point out that known bounds for CFTs with internal U(1) symmetries readily apply to unitary WCFTs.