scholarly journals TWISTED QUANTUM FIELDS ON MOYAL AND WICK–VOROS PLANES ARE INEQUIVALENT

2009 ◽  
Vol 24 (22) ◽  
pp. 1721-1730 ◽  
Author(s):  
A. P. BALACHANDRAN ◽  
M. MARTONE
Keyword(s):  
Field Theories ◽  
Gauge Fields ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Poincaré Group ◽  
Energy Diagram ◽  
Poincare Group ◽  
Self Energy ◽  
Moyal Plane ◽  
Noncommutative Parameter

The Moyal and Wick–Voros planes [Formula: see text] are *-isomorphic. On each of these planes the Poincaré group acts as a Hopf algebra symmetry if its coproducts are deformed by twist factors [Formula: see text]. We show that the *-isomorphism [Formula: see text] also does not map the corresponding twists of the Poincaré group algebra. The quantum field theories on these planes with twisted Poincaré–Hopf symmetries are thus inequivalent. We explicitly verify this result by showing that a nontrivial dependence on the noncommutative parameter is present for the Wick–Voros plane in a self-energy diagram whereas it is known to be absent on the Moyal plane (in the absence of gauge fields).1–3 Our results differ from those of Ref. 4 because of differences in the treatments of quantum field theories.

scholarly journals Supersymmetry: Early Roots That Did Not Grow

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Cecilia Jarlskog
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Poincaré Group ◽  
Poincare Group

This paper is about early roots of supersymmetry, as found in the literature from 1940s and early 1950s. There were models where the power of “partners” in alleviating divergences in quantum field theory was recognized. However, other currently known remarkable features of supersymmetry, such as its role in the extension of the Poincaré group, were not known. There were, of course, no supersymmetric nonabelian quantum field theories in those days.

scholarly journals Emergent fields from hidden sectors

2021 ◽  
Vol 2105 (1) ◽  
pp. 012002
Author(s):  
Pascal Anastasopoulos
Keyword(s):  
String Theory ◽  
Particle Physics ◽  
Field Theories ◽  
Gauge Fields ◽  
Quantum Field Theories ◽  
Quantum Field

Abstract The present research proceeding aims at investigating/exploring/sharpening the phenomenological consequences of string theory and holography in particle physics and cosmology. We rely on and elaborate on the recently proposed framework whereby four-dimensional quantum field theories describe all interactions in Nature, and gravity is an emergent and not a fundamental force. New gauge fields, axions, and fermions, which can play the role of right-handed neutrinos, can also emerge in this framework. Preprint: UWThPh 2021-8

scholarly journals A web of 2d dualities: ${\bf Z}_2$ gauge fields and Arf invariants

2019 ◽  
Vol 7 (1) ◽  
Author(s):  
Andreas Karch ◽  
David Tong ◽  
Carl Turner
Keyword(s):  
Global Symmetries ◽  
Spin Structure ◽  
Field Theories ◽  
Gauge Fields ◽  
Dirac Fermion ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Modular Invariant ◽  
Wigner Transformation ◽  
The Web

We describe a web of well-known dualities connecting quantum field theories in d=1+1 dimensions. The web is constructed by gauging Z_2Z2 global symmetries and includes a number of perennial favourites such as the Jordan-Wigner transformation, Kramers-Wannier duality, bosonization of a Dirac fermion, and T-duality. There are also less-loved examples, such as non-modular invariant c=1 CFTs that depend on a background spin structure.

scholarly journals NONCOMMUTATIVE THERMOFIELD DYNAMICS

2010 ◽  
Vol 25 (16) ◽  
pp. 3209-3220 ◽  
Author(s):  
MARCELO L. COSTA ◽  
AMILCAR R. QUEIROZ ◽  
ADEMIR E. SANTANA
Keyword(s):  
Field Theories ◽  
Effect Of Temperature ◽  
Integral Approach ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Point Function ◽  
Operator Formalism ◽  
Noncommutative Spaces ◽  
The One ◽  
Noncommutative Parameter

The real-time operator formalism for thermal quantum field theories, thermofield dynamics, is formulated in terms of a path-integral approach in noncommutative spaces. As an application, the two-point function for a thermal noncommutative λϕ4 theory is derived at the one-loop level. The effect of temperature and the noncommutative parameter, competing with one another, is analyzed.

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 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.

scholarly journals Applying the Variational Principle to (1+1)-Dimensional Quantum Field Theories

2010 ◽  
Vol 105 (25) ◽  
Author(s):  
Jutho Haegeman ◽  
J. Ignacio Cirac ◽  
Tobias J. Osborne ◽  
Henri Verschelde ◽  
Frank Verstraete
Keyword(s):  
Variational Principle ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field
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