scholarly journals Frame covariant formalism for fermionic theories

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Kieran Finn ◽  
Sotirios Karamitsos ◽  
Apostolos Pilaftsis
Keyword(s):  
Effective Action ◽  
Degrees Of Freedom ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Covariant Formalism ◽  
Classical Action ◽  
Proper Definition ◽  
Definition Of ◽  
Standing Problem

AbstractWe present a frame- and reparametrisation-invariant formalism for quantum field theories that include fermionic degrees of freedom. We achieve this using methods of field-space covariance and the Vilkovisky–DeWitt (VDW) effective action. We explicitly construct a field-space supermanifold on which the quantum fields act as coordinates. We show how to define field-space tensors on this supermanifold from the classical action that are covariant under field reparametrisations. We then employ these tensors to equip the field-space supermanifold with a metric, thus solving a long-standing problem concerning the proper definition of a metric for fermionic theories. With the metric thus defined, we use well-established field-space techniques to extend the VDW effective action and express any fermionic theory in a frame- and field-reparametrisation-invariant manner.

A NOTE ON DUALITY, FROBENIUS ALGEBRAS AND TQFTS

2004 ◽  
Vol 13 (08) ◽  
pp. 999-1006
Author(s):  
LUCIAN M. IONESCU
Keyword(s):  
Monoidal Category ◽  
The Self ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Self Duality ◽  
Frobenius Algebras ◽  
Topological Quantum ◽  
Definition Of ◽  
Hermitian Structures

Topological quantum field theories (TQFTs) represent the structure present in cobordism categories. As an example, we review the correspondence between Frobenius algebras and (1+1)TQFTs. It is a corollary of the self-duality of the cobordism category, which is a rigid monoidal category generated by a Frobenius object (the circle). A self-dual definition of a Frobenius object without the use of a prefered dual is considered. The issue of duality as part of the definition of a TQFT is addressed. Note that duality is preserved by monoidal functors. Hermitian structures are modeled as a conjugation compatible with duality. It is the structure cobordism categories posses. A definition of generalized cobordism categories is proposed.

scholarly journals Wilsonian Effective Action and Entanglement Entropy

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1221
Author(s):  
Satoshi Iso ◽  
Takato Mori ◽  
Katsuta Sakai
Keyword(s):  
Renormalization Group ◽  
Gauge Theory ◽  
Effective Action ◽  
Correlation Functions ◽  
Entanglement Entropy ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Non Gaussian

This is a continuation of our previous works on entanglement entropy (EE) in interacting field theories. In previous papers, we have proposed the notion of ZM gauge theory on Feynman diagrams to calculate EE in quantum field theories and shown that EE consists of two particular contributions from propagators and vertices. We have also shown that the purely non-Gaussian contributions from interaction vertices can be interpreted as renormalized correlation functions of composite operators. In this paper, we will first provide a unified matrix form of EE containing both contributions from propagators and (classical) vertices, and then extract further non-Gaussian contributions based on the framework of the Wilsonian renormalization group. It is conjectured that the EE in the infrared is given by a sum of all the vertex contributions in the Wilsonian effective action.

scholarly journals Anti-Newtonian Expansions and the Functional Renormalization Group

Universe ◽  
2019 ◽  
Vol 5 (3) ◽  
pp. 85 ◽  
Author(s):  
Max Niedermaier
Keyword(s):  
Renormalization Group ◽  
Degrees Of Freedom ◽  
World Line ◽  
Newtonian Limit ◽  
Field Theories ◽  
Quantum Mechanical ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Functional Renormalization Group ◽  
Scalar Quantum

Anti-Newtonian expansions are introduced for scalar quantum field theories and classical gravity. They expand around a limiting theory that evolves only in time while the spatial points are dynamically decoupled. Higher orders of the expansion re-introduce spatial interactions and produce overlapping lightcones from the limiting isolated world line evolution. In scalar quantum field theories, the limiting system consists of copies of a self-interacting quantum mechanical system. In a spatially discretized setting, a nonlinear “graph transform” arises that produces an in principle exact solution of the Functional Renormalization Group for the Legendre effective action. The quantum mechanical input data can be prepared from its 1 + 0 dimensional counterpart. In Einstein gravity, the anti-Newtonian limit has no dynamical spatial gradients, yet remains fully diffeomorphism invariant and propagates the original number of degrees of freedom. A canonical transformation (trivialization map) is constructed, in powers of a fractional inverse of Newton’s constant, that maps the ADM action into its anti-Newtonian limit. We outline the prospects of an associated trivializing flow in the quantum theory.

scholarly journals QUANTUM FIELD THEORIES ON NULL SURFACES

2001 ◽  
Vol 16 (10) ◽  
pp. 1789-1808
Author(s):  
KUMAR S. GUPTA ◽  
BADIS YDRI
Keyword(s):  
Degrees Of Freedom ◽  
The Self ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Limiting Behavior ◽  
Duality Symmetry ◽  
Null Surface ◽  
Free Scalar ◽  
Null Surfaces

We study the behavior of quantum field theories defined on a surface S as it tends to a null surface Sn. In the case of a real, free scalar field theory the above limiting procedure reduces the system to one with a finite number of degrees of freedom. This system is shown to admit a one parameter family of inequivalent quantizations. A duality symmetry present in the model can be used to remove the quantum ambiguity at the self-dual point. In the case of the nonlinear σ-model with the Wess–Zumino–Witten term a similar limiting behavior is obtained. The quantization ambiguity in this case however cannot be removed by any means.

scholarly journals Mei Symmetry and Invariants of Quasi-Fractional Dynamical Systems with Non-Standard Lagrangians

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 1061 ◽  
Author(s):  
Zhang ◽  
Wang
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Small Disturbance ◽  
Definition Of ◽  
Disturbed Motion ◽  
Mei Symmetry

Non-standard Lagrangians play an important role in the systems of non-conservative dynamics or nonlinear differential equations, quantum field theories, etc. This paper deals with quasi-fractional dynamical systems from exponential non-standard Lagrangians and power-law non-standard Lagrangians. Firstly, the definition, criterion, and corresponding new conserved quantity of Mei symmetry in this system are presented and studied. Secondly, considering that a small disturbance is applied on the system, the differential equations of the disturbed motion are established, the definition of Mei symmetry and corresponding criterion are given, and the new adiabatic invariants led by Mei symmetry are proposed and proved. Examples also show the validity of the results.

Symmetries: From classical to quantum field theories

2019 ◽  
pp. 265-282
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Gauge Theories ◽  
Invariant Solution ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Dirac Fermions ◽  
Quantum Field ◽  
Classical Action ◽  
Quantum Operator ◽  
Domain Wall Fermions ◽  
Lattice Regularization

Chapter 16 deals with the important problem of quantization with symmetries, that is, how to implement symmetries of the classical action in the corresponding quantum theory. The proposed solutions are based on methods like regularization by addition of higher order derivatives or regulator fields, or lattice regularization. Difficulties encountered in the case of chiral theories are emphasized. This may lead to obstacles for symmetric quantization called anomalies. Examples can be found in the case of chiral gauge theories. Their origin can be traced to the problem of quantum operator ordering in products. A non–perturbative regularization, also useful for numerical simulations, is based on introducing a space lattice. Difficulties appear for lattice Dirac fermions, leading the fermion doubling problem. Wilson’s fermions provide a non–chiral invariant solution. Chiral invariant solutions have been found, called overlap fermions or domain wall fermions.

scholarly journals RENORMALIZATION GROUP IMPROVING THE EFFECTIVE ACTION: A REVIEW

1999 ◽  
Vol 14 (10) ◽  
pp. 1485-1521 ◽  
Author(s):  
DAVID HOCHBERG ◽  
JUAN PÉREZ-MERCADER ◽  
CARMEN MOLINA-PARÍS ◽  
MATT VISSER
Keyword(s):  
Renormalization Group ◽  
Effective Action ◽  
Stochastic Systems ◽  
Scale Dependence ◽  
Tree Level ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Statistical Nature ◽  
Classical Action ◽  
Renormalization Group Equations

The existence of fluctuations together with interactions leads to scale-dependence, in the couplings of quantum field theories for the case of quantum fluctuations, and in the couplings of stochastic systems when the fluctuations are of a thermal or statistical nature. In both cases the effects of these fluctuations can be accounted for by solutions of the corresponding renormalization group equations. In this review, we show how the renormalization group equations are intimately connected with the effective action: given the effective action we can trivially extract the renormalization group equations; given the renormalization group equations the effects of these fluctuations can be included in the classical action by using what is known as improved perturbation theory (wherein the bare parameters appearing in tree-level expressions are replaced by their scale-dependent running forms). The improved action can then be used to reconstruct the effective action, up to finite renormalizations, and up to gradient terms.

Dynamical degrees of freedom of constrained quantum field theories (?-model)

1985 ◽  
Vol 28 (4) ◽  
pp. 587-589
Author(s):  
F. Alonso ◽  
J. Julve ◽  
A. Tiemblo ◽  
R. Tresguerres
Keyword(s):  
Degrees Of Freedom ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Dynamical Degrees

scholarly journals Formfactors of Relativistic Composite Particle Interactions in Unified Nonlinear Spinorfield Models

1985 ◽  
Vol 40 (7) ◽  
pp. 752-773
Author(s):  
H. Stumpf
Keyword(s):  
Composite Particle ◽  
Particle Interaction ◽  
High Energy ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Statistical Interpretation ◽  
Quantum Field ◽  
Mapping Procedure ◽  
Effective Dynamics ◽  
Rough Approximation

Unified nonlinear spinorfield models are self-regularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined and below the threshold of preon production the effective dynamics of the model is only concerned with bound state reactions. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived and the effective dynamics for preon-antipreon boson states and three preon-fermion states (with corresponding anti-fermions) was studied in the low energy limit. The transformation of the functional energy representation of the spinorfield into composite particle functional operators produced a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. In this paper these calculations are extended into the high energy range. This leads to formfactors for the composite particle interaction terms which are calculated in a rough approximation and which in principle are observable. In addition, the mathematical and physical interpretation of nonlocal quantum field theories and the meaning of the mapping procedure, its relativistic invariance etc. are discussed.

scholarly journals Categorification of algebraic quantum field theories

2021 ◽  
Vol 111 (2) ◽  
Author(s):  
Marco Benini ◽  
Marco Perin ◽  
Alexander Schenkel ◽  
Lukas Woike
Keyword(s):  
Universal Algebra ◽  
Finite Groups ◽  
Physical Interpretation ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Algebraic Quantum

AbstractThis paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary AQFTs embed as a coreflective full 2-subcategory into the 2-category of 2AQFTs. Examples of 2AQFTs that do not come from ordinary AQFTs via this embedding are constructed by a local gauging construction for finite groups, which admits a physical interpretation in terms of orbifold theories. A categorification of Fredenhagen’s universal algebra is developed and also computed for simple examples of 2AQFTs.

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