Quantum Field Theory In Terms Research Articles

FeynMG: A FeynRules extension for scalar-tensor theories of gravity

The ability to represent perturbative expansions of interacting quantum field theories in terms of simple diagrammatic rules has revolutionized calculations in particle physics (and elsewhere). Moreover, these rules are readily automated, a process that has catalyzed the rise of symbolic algebra packages. However, in the case of extended theories of gravity, such as scalar-tensor theories, it is necessary to precondition the Lagrangian to apply this automation or, at the very least, to take advantage of existing software pipelines. We present a Mathematica code FeynMG, which works in conjunction with the well-known package FeynRules, to do just that: FeynMG takes as inputs the FeynRules model file for a non-gravitational theory and a user-supplied gravitational Lagrangian. FeynMG provides functionality that inserts the minimal gravitational couplings of the degrees of freedom specified in the model file, determines the couplings of the additional tensor and scalar degrees of freedom (the metric and the scalar field from the gravitational sector), and preconditions the resulting Lagrangian so that it can be passed to FeynRules, either directly or by outputting an updated FeynRules model file. The Feynman rules can then be determined and output through FeynRules, using existing universal output formats and interfaces to other analysis packages. Program summaryProgram title: FeynMGCPC Library link to program files:https://doi.org/10.17632/bjpfmtt55k.1Developer's repository link:https://gitlab.com/feynmg/FeynMGLicensing provisions: MIT licenseProgramming language:Mathematica 13.2Nature of problem: Determining the additional interactions that scalar-tensor theories of gravity induce between the fields of the Standard Model of particle physics and its extensions is a tedious and time-consuming task that is ripe for automation. FeynMG is a package that provides this automation. It can expand the spacetime metric around a flat background and perform the necessary field redefinitions for a given theory in order to provide a Lagrangian that is in a form that can be processed by FeynRules[1]. The Feynman rules for the theory can then be determined using the existing functionality of FeynRules and output in formats that can be read into other particle-physics analysis packages.Solution method: (1) Load both FeynRules and FeynMG into Mathematica. (2) Load a model file describing a given matter sector and Lagrangian. (3) Use the FeynMG implementation to: (3a) append the gravitational sector and incorporate curvature-dependent objects, such as the metric, curvature scalars and tensors, and covariant derivatives; (3b) effect a Weyl transformation or expand the spacetime metric up to second order in graviton interactions with the matter fields; and (3c) diagonalize mass and kinetic mixings, and canonically normalize dynamical fields. (4) Pass the output directly to FeynRules or output a new model file from FeynMG.

Scattering in Algebraic Approach to Quantum Theory—Associative Algebras

The definitions of scattering matrix and inclusive scattering matrix in the framework of formulation of quantum field theory in terms of associative algebras with involution are presented. The scattering matrix is expressed in terms of Green functions on shell (LSZ formula), and the inclusive scattering matrix is expressed in terms of generalized Green functions on shell. The expression for inclusive scattering matrix can be used also for quasi-particles (for elementary excitations of any translation-invariant stationary state, for example, for elementary excitations of equilibrium state). An interesting novelty is the consideration of associative algebras over real numbers.

Chiral Waves and Topological Novel States in Fermi

This first show was that the spin system, the two nearest neighbour spin in the Entanglement of measuring compliance by the ground conditions are achieved Berry stage to the relation when it is a closed path developed is. It noted the need to share the stage in a kind of geometric phase as explained to go to which any deformations involved is not and it’s the first Stiefel-Whitney class which is to Z_z–cohomology value takes. However for polarized fermions we can relate the exchange phase as the celebrated Berry phase as in this case the Z_z-cohomology becomes irrelevant and is consistent with the first Chern class which involves curvature. This follows from the depiction of a fermion as a scalar particle attached with a magnetic flux line. As in this framework the measure of entanglement of two nearest neighbor spins in a spin system given by concurrence is found to be associated with the Berry phase acquired by a spin state when it evolves in a closed path we can consider that entanglement is a consequence of Fermi statistics. It has been noted that in terms of quantum field theory, the berry phase is related to the perpetual inconsistency caused by the breaking of the perpetual symmetry. As mentioned earlier the quantization procedure of a fermion in the framework of Nelson’s stochastic quantization procedure introduces an internal variable which appears as a direction vector and gives rise to spin degrees of freedom. It's pointing to is that when a spin- 1 state of two spin 1/2 state is a Entangle system as considered to be that, the most widely covered state longitudinal elements with the matching it.

Scaling Limits of Lattice Quantum Fields by Wavelets

We present a rigorous renormalization group scheme for lattice quantum field theories in terms of operator algebras. The renormalization group is considered as an inductive system of scaling maps between lattice field algebras. We construct scaling maps for scalar lattice fields using Daubechies’ wavelets, and show that the inductive limit of free lattice ground states exists and the limit state extends to the familiar massive continuum free field, with the continuum action of spacetime translations. In particular, lattice fields are identified with the continuum field smeared with Daubechies’ scaling functions. We compare our scaling maps with other renormalization schemes and their features, such as the momentum shell method or block-spin transformations.

⋆-cohomology, third type Chern character and anomalies in general translation-invariant noncommutative Yang–Mills

A representation of general translation-invariant star products ⋆ in the algebra of [Formula: see text] is introduced which results in the Moyal–Weyl–Wigner quantization. It provides a matrix model for general translation-invariant noncommutative quantum field theories in terms of the noncommutative calculus on differential graded algebras. Upon this machinery a cohomology theory, the so-called ⋆-cohomology, with groups [Formula: see text], [Formula: see text], is worked out which provides a cohomological framework to formulate general translation-invariant noncommutative quantum field theories based on the achievements for the commutative fields, and is comparable to the Seiberg–Witten map for the Moyal case. Employing the Chern–Weil theory via the integral classes of [Formula: see text] a noncommutative version of the Chern character is defined as an equivariant form which contains topological information about the corresponding translation-invariant noncommutative Yang–Mills theory. Thereby, we study the mentioned Yang–Mills theories with three types of actions of the gauge fields on the spinors, the ordinary, the inverse, and the adjoint action, and then some exact solutions for their anomalous behaviors are worked out via employing the homotopic correlation on the integral classes of ⋆-cohomology. Finally, the corresponding consistent anomalies are also derived from this topological Chern character in the ⋆-cohomology.

Higher form symmetries and M-theory

We discuss the geometric origin of discrete higher form symmetries of quantum field theories in terms of defect groups from geometric engineering in M-theory. The flux non-commutativity in M-theory gives rise to (mixed) ’t Hooft anomalies for the defect group which constrains the corresponding global structures of the associated quantum fields. We analyze the example of 4d mathcal{N} = 1 SYM gauge theory in four dimensions, and we reproduce the well-known classification of global structures from reading between its lines. We extend this analysis to the case of 7d mathcal{N} = 1 SYM theory, where we recover it from a mixed ’t Hooft anomaly among the electric 1-form center symmetry and the magnetic 4-form center symmetry in the defect group. The case of five-dimensional SCFTs from M-theory on toric singularities is discussed in detail. In that context we determine the corresponding 1-form and 2-form defect groups and we explain how to determine the corresponding mixed ’t Hooft anomalies from flux non-commutativity. Several predictions for non-conventional 5d SCFTs are obtained. The matching of discrete higher-form symmetries and their anomalies provides an interesting consistency check for 5d dualities.

Parallel transport of higher flat gerbes as an extended homotopy quantum field theory

We prove that the parallel transport of a flat \(n-1\)-gerbe on any given target space gives rise to an n-dimensional extended homotopy quantum field theory. In case the target space is the classifying space of a finite group, we provide explicit formulae for this homotopy quantum field theory in terms of transgression. Moreover, we use the geometric theory of orbifolds to give a dimension-independent version of twisted and equivariant Dijkgraaf–Witten models. Finally, we introduce twisted equivariant Dijkgraaf–Witten theories giving us in the 3-2-1-dimensional case a new class of equivariant modular tensor categories which can be understood as twisted versions of the equivariant modular categories constructed by Maier, Nikolaus and Schweigert.

An invitation to 2D TQFT and quantization of Hitchin spectral curves

This article consists of two parts. In Part 1, we present a formulation of two-dimensional topological quantum field theories in terms of a functor from a category of Ribbon graphs to the endofuntor category of a monoidal category. The key point is that the category of ribbon graphs produces all Frobenius objects. Necessary backgrounds from Frobenius algebras, topological quantum field theories, and cohomological field theories are reviewed. A result on Frobenius algebra twisted topological recursion is included at the end of Part 1. In Part 2, we explain a geometric theory of quantum curves. The focus is placed on the process of quantization as a passage from families of Hitchin spectral curves to families of opers. To make the presentation simpler, we unfold the story using SL_2(\mathbb{C})-opers and rank 2 Higgs bundles defined on a compact Riemann surface $C$ of genus greater than $1$. In this case, quantum curves, opers, and projective structures in $C$ all become the same notion. Background materials on projective coordinate systems, Higgs bundles, opers, and non-Abelian Hodge correspondence are explained.

A Persistent Particle Ontology for Quantum Field Theory in Terms of the Dirac Sea

We show that the Bohmian approach in terms of persisting particles that move on continuous trajectories following a deterministic law can be literally applied to QFT. By means of the Dirac sea model – exemplified in the electron sector of the standard model neglecting radiation – we explain how starting from persisting particles, one is led to standard QFT employing creation and annihilation operators when tracking the dynamics with respect to a reference state, the so-called vacuum. Since on the level of wave functions, both formalisms are mathematically equivalent, this proposal provides for an ontology of QFT that includes a dynamics of individual processes, solves the measurement problem and explains the appearance of creation and annihilation events.

Physics Without Physics

David Finkelstein was very fond of the new information-theoretic paradigm of physics advocated by John Archibald Wheeler and Richard Feynman. Only recently, however, the paradigm has concretely shown its full power, with the derivation of quantum theory (Chiribella et al., Phys. Rev. A 84:012311, 2011; D'Ariano et al., 2017) and of free quantum field theory (D'Ariano and Perinotti, Phys. Rev. A 90:062106, 2014; Bisio et al., Phys. Rev. A 88:032301, 2013; Bisio et al., Ann. Phys. 354:244, 2015; Bisio et al., Ann. Phys. 368:177, 2016) from informational principles. The paradigm has opened for the first time the possibility of avoiding physical primitives in the axioms of the physical theory, allowing a refoundation of the whole physics over logically solid grounds. In addition to such methodological value, the new information-theoretic derivation of quantum field theory is particularly interesting for establishing a theoretical framework for quantum gravity, with the idea of obtaining gravity itself as emergent from the quantum information processing, as also suggested by the role played by information in the holographic principle (Susskind, J. Math. Phys. 36:6377, 1995; Bousso, Rev. Mod. Phys. 74:825, 2002). In this paper I review how free quantum field theory is derived without using mechanical primitives, including space-time, special relativity, Hamiltonians, and quantization rules. The theory is simply provided by the simplest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the three following simple principles: homogeneity, locality, and isotropy. The inherent discrete nature of the informational derivation leads to an extension of quantum field theory in terms of a quantum cellular automata and quantum walks. A simple heuristic argument sets the scale to the Planck one, and the observed regime is that of small wavevectors ...

Classical versus quantum completeness

The notion of quantum-mechanical completeness is adapted to situations where the only adequate description is in terms of quantum field theory in curved space-times. It is then shown that Schwarzschild black holes, although geodesically incomplete, are quantum complete.

Dynamical Locality of the Free Maxwell Field

We consider the non-interacting source-free Maxwell field, described both in terms of the vector potential and the field strength. Starting from the classical field theory on contractible globally hyperbolic spacetimes, we extend the classical field theory to general globally hyperbolic spacetimes in two ways to obtain a "universal" theory and a "reduced" theory. The quantum field theory in terms of the unital $*$-algebra of the smeared quantum field is then obtained by an application of a suitable quantisation functor. We show that the universal theories fail local covariance and dynamical locality owing to the possibility of having non-trivial radicals in the classical and non-trivial centres in the quantum case. The reduced theories are both locally covariant and dynamically local. These models provide new examples relevant to the discussion of how theories should be formulated so as to describe the same physics in all spacetimes.

Entanglement entropy and gravity/condensed matter correspondence

The entanglement entropy has been very important in various subjects such as the quantum information theory, condensed matter physics and quantum gravity. Especially, for more than twenty years, this quantity has been studied by many people in order to obtain a quantum mechanical interpretation of the gravitational entropy such as the black hole entropy. We will introduce recent progresses toward this long-standing problem in quantum gravity by applying the idea of holography, especially the AdS/CFT correspondence found in string theory. We will explain the holographic formula which computes the entanglement entropy of quantum field theories in terms of the area of minimal surfaces in general relativity. We will also review the recent application of AdS/CFT correspondence to condensed matter physics from the viewpoint of entanglement entropy.

Counterterms in the context of the universal Hopf algebra of renormalization

The manuscript discovers a new interpretation of counterterms of renormalizable Quantum Field Theories in terms of formal expansions of decorated rooted trees.

Multi-time formulation of pair creation

In a recent work (Petrat and Tumulka 2013 arXiv:1309.0802), we have described a formulation of a model quantum field theory in terms of a multi-time wave function and proposed a suitable system of multi-time Schrödinger equations governing the evolution of that wave function. Here, we provide further evidence that multi-time wave functions provide a viable formulation of relevant quantum field theories by describing a multi-time formulation, analogous to the one in Petrat and Tumulka (2013 arXiv:1309.0802), of another model quantum field theory. This model involves three species of particles, say x-particles, anti-x-particles, and y-particles, and postulates that a y-particle can decay into a pair consisting of an x and an anti-x particle, and that an x–anti-x pair, when they meet, annihilate each other creating a y-particle. (Alternatively, the model can also be interpreted as representing beta decay.) The wave function is a multi-time version of a time-dependent state vector in Fock space (or rather, the appropriate product of Fock spaces) in the particle-position representation. We write down multi-time Schrödinger equations and verify that they are consistent, provided that an even number of the three particle species involved are fermionic.

NEW CANDIDATES FOR A HERMITIAN APPROACH OF GRAVITY

In this paper, some possible candidates for the study of gravity are proposed in terms of complex Finsler geometry. These mainly concern the complex Hermitian versions of weakly gravitational metric and Schwarzschild metric. For the weakly gravitational fields, we state few interesting geometrical and physical aspects such as the conditions under which a complex Finsler metrics are projectively related to the weakly gravitational metric. In the Kähler case, the geodesic curves of the weakly gravitational metric are obtained. Some applications concerning the deformations of the weakly gravitational Hermitian metric to a complex Randers metric are described. Another candidate for gravity is given by so-called Hermitian Schwarzschild metric for which some geodesic curves are highlighted. The last part of the paper is devoted to a generalization of the complex Klein–Gordon equations, in terms of Quantum field theory on a curved space.

Holographic Quantum States

We show how continuous matrix product states of quantum fields can be described in terms of the dissipative nonequilibrium dynamics of a lower-dimensional auxiliary boundary field by demonstrating that the spatial correlation functions of the bulk field correspond to the temporal statistics of the boundary field. This equivalence (1) illustrates an intimate connection between the theory of continuous quantum measurement and quantum field theory, (2) gives an explicit construction of the boundary field allowing the extension of real-space renormalization group methods to arbitrary dimensional quantum field theories without the introduction of a lattice parameter, and (3) yields a novel interpretation of recent cavity QED experiments in terms of quantum field theory, and hence paves the way toward observing genuine quantum phase transitions in such zero-dimensional driven quantum systems.

Particle creation in Bose-Einstein condensates: Theoretical formulation based on conserving gapless mean-field theory

We formulate particle creation phenomena in Bose--Einstein condensates in terms of conserving gapless mean field theory for weakly interacting Bose gases. The particle creation spectrum is calculated by rediagonalizing the Bogoliubov--de Gennes (BdG) Hamiltonian in mean field theory. The conservation implies that quasiparticle creation is accompanied by quantum backreaction to the condensates. Particle creation in this mean field theory is found to be equivalent to that in quantum field theory (QFT) in curved spacetime. An expression is obtained for an effective metric affected by quantum backreaction. The formula for the particle creation spectrum obtained in terms of QFT in curved spacetime is shown to be the same as that given by rediagonalizing the BdG Hamiltonian.

The principle of locality: Effectiveness, fate, and challenges

The special theory of relativity and quantum mechanics merge in the key principle of quantum field theory, the principle of locality. We review some examples of its “unreasonable effectiveness” in giving rise to most of the conceptual and structural frame of quantum field theory, especially in the absence of massless particles. This effectiveness shows up best in the formulation of quantum field theory in terms of operator algebras of local observables; this formulation is successful in digging out the roots of global gauge invariance, through the analysis of superselection structure and statistics, in the structure of the local observable quantities alone, at least for purely massive theories; but so far it seems unfit to cope with the principle of local gauge invariance. This problem emerges also if one attempts to figure out the fate of the principle of locality in theories describing the gravitational forces between elementary particles as well. An approach based on the need to keep an operational meaning, in terms of localization of events, of the notion of space-time, shows that, in the small, the latter must loose any meaning as a classical pseudo-Riemannian manifold, locally based on Minkowski space, but should acquire a quantum structure at the Planck scale. We review the geometry of a basic model of quantum space-time and some attempts to formulate interaction of quantum fields on quantum space-time. The principle of locality is necessarily lost at the Planck scale, and it is a crucial open problem to unravel a replacement in such theories which is equally mathematically sharp, namely, a principle where the general theory of relativity and quantum mechanics merge, which reduces to the principle of locality at larger scales. Besides exploring its fate, many challenges for the principle of locality remain; among them, the analysis of superselection structure and statistics also in the presence of massless particles, and to give a precise mathematical formulation to the measurement process in local and relativistic terms; for which we outline a qualitative scenario which avoids the Einstein, Podolski, and Rosen paradox.

Axiomatic Quantum Field Theory in Terms of Operator Product Expansions: General Framework, and Perturbation Theory via Hochschild Cohomology

In this paper, we propose a new framework for quantum field theory in terms of consistency conditions. The consistency conditions that we consider are associativity or factorization conditions on the operator product expansion (OPE) of the theory, and are proposed to be the defining property of any quantum field theory. Our framework is presented in the Euclidean setting, and is applicable in principle to any quantum field theory, including non-conformal ones. In our framework, we obtain a characterization of perturbations of a given quantum field theory in terms of a certain cohomology ring of Hochschild-type. We illustrate our framework by the free field, but our constructions are general and apply also to interacting quantum field theories. For such theories, we propose a new scheme to construct the OPE which is based on the use of non-linear quantized field equations.