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 LECTURE NOTES ON INTERACTING QUANTUM FIELDS IN DE SITTER SPACE

2014 ◽  
Vol 23 (01) ◽  
pp. 1430001 ◽  
Author(s):  
E. T. AKHMEDOV
Keyword(s):  
De Sitter Space ◽  
The Self ◽  
Field Theories ◽  
Tree Level ◽  
Main Concern ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Quantum Fields ◽  
De Sitter ◽  
Invariant States

We discuss peculiarities of quantum fields in de Sitter (dS) space on the example of the self-interacting massive real scalar, minimally coupled to the gravity background. Nonconformal quantum field theories (QFTs) in dS space show very special infrared behavior, which is not shared by quantum fields neither in flat nor in anti-dS space: in dS space loops are not suppressed in comparison with tree level contributions because there are strong infrared corrections. That is true even for massive fields. Our main concern is the interrelation between these infrared effects, the invariance of the QFT under the dS isometry and the (in)stability of dS invariant states (and of dS space itself) under nonsymmetric perturbations.

scholarly journals Entropy on a null surface for interacting quantum field theories and the Bousso bound

2015 ◽  
Vol 91 (8) ◽  
Author(s):  
Raphael Bousso ◽  
Horacio Casini ◽  
Zachary Fisher ◽  
Juan Maldacena
Keyword(s):  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Null Surface

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 ON GENERALIZED SELF-DUALITY EQUATIONS TOWARDS SUPERSYMMETRIC QUANTUM FIELD THEORIES OF FORMS

1998 ◽  
Vol 13 (14) ◽  
pp. 1115-1132 ◽  
Author(s):  
LAURENT BAULIEU ◽  
CÉLINE LAROCHE
Keyword(s):  
The Self ◽  
Field Theories ◽  
Gauge Fields ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Time Dimension ◽  
Yang Mills ◽  
Self Duality ◽  
Topological Quantum ◽  
Gauge Functions

We classify possible "self-duality" equations for p-form gauge fields in space–time dimension up to D=16, generalizing the pioneering work of Corrigan et al. (1982) on Yang–Mills fields (p=1) in 4<D≤8. We impose two crucial requirements. First, there should exist a 2(p+1)-form T-invariant under a subgroup H of SO D. Second, the representation for the SO D curvature of the gauge field must decompose under H in a relevant way. When these criteria are fulfilled, the "self-duality" equations can be candidates of gauge functions for SO D-covariant and H-invariant topological quantum field theories. Intriguing possibilities occur for D≥10 for various p-form gauge fields.

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 ENDOMORPHISMS AND AUTOMORPHISMS OF LOCALLY COVARIANT QUANTUM FIELD THEORIES

2013 ◽  
Vol 25 (05) ◽  
pp. 1350008 ◽  
Author(s):  
CHRISTOPHER J. FEWSTER
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Automorphism Group ◽  
Scalar Fields ◽  
Field Theories ◽  
Covariant Theory ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Covariant Quantum ◽  
Free Scalar

In the framework of locally covariant quantum field theory, a theory is described as a functor from a category of spacetimes to a category of *-algebras. It is proposed that the global gauge group of such a theory can be identified as the group of automorphisms of the defining functor. Consequently, multiplets of fields may be identified at the functorial level. It is shown that locally covariant theories that obey standard assumptions in Minkowski space, including energy compactness, have no proper endomorphisms (i.e. all endomorphisms are automorphisms) and have a compact automorphism group. Further, it is shown how the endomorphisms and automorphisms of a locally covariant theory may, in principle, be classified in any single spacetime. As an example, the endomorphisms and automorphisms of a system of finitely many free scalar fields are completely classified.

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.

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