Quantum Field Theories on Lattice: (i) QCD Topology, and (ii) Non-perturbative Gauge-Fixing

2018 ◽  
Vol 59 (5) ◽  
Author(s):  
Asit K. De
Keyword(s):  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Gauge Fixing

GENERAL COVARIANCE, TOPOLOGICAL QUANTUM FIELD THEORIES AND FRACTIONAL STATISTICS

1992 ◽  
Vol 07 (02) ◽  
pp. 209-234 ◽  
Author(s):  
J. GAMBOA
Keyword(s):  
Hamiltonian Formalism ◽  
Field Theories ◽  
General Covariance ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Fractional Statistics ◽  
Multiply Connected ◽  
Topological Quantum ◽  
Gauge Fixing ◽  
Topological Quantum Field Theories

Topological quantum field theories and fractional statistics are both defined in multiply connected manifolds. We study the relationship between both theories in 2 + 1 dimensions and we show that, due to the multiply-connected character of the manifold, the propagator for any quantum (field) theory always contains a first order pole that can be identified with a physical excitation with fractional spin. The article starts by reviewing the definition of general covariance in the Hamiltonian formalism, the gauge-fixing problem and the quantization following the lines of Batalin, Fradkin and Vilkovisky. The BRST–BFV quantization is reviewed in order to understand the topological approach proposed here.

scholarly journals BRST FIELD THEORY OF RELATIVISTIC PARTICLES

1992 ◽  
Vol 07 (28) ◽  
pp. 7119-7134 ◽  
Author(s):  
J.W. VAN HOLTEN
Keyword(s):  
Field Theory ◽  
Correlation Functions ◽  
Relativistic Particle ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Wave Operators ◽  
Brst Operator ◽  
Gauge Fixing ◽  
Relativistic Particles

A generalization of BRST field theory is presented, based on wave operators for the fields constructed out of, but different from the BRST operator. We discuss their quantization, gauge fixing and the derivation of propagators. We show, that the generalized theories are relevant to relativistic particle theories in the Brink-Di Vecchia-Howe-Polyakov (BDHP) formulation, and argue that the same phenomenon holds in string theories. In particular it is shown, that the naive BRST formulation of the BDHP theory leads to trivial quantum field theories with vanishing correlation functions.

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 A C*-algebraic Approach to Interacting Quantum Field Theories

2020 ◽  
Vol 377 (2) ◽  
pp. 947-969 ◽  
Author(s):  
Detlev Buchholz ◽  
Klaus Fredenhagen
Keyword(s):  
Algebraic Approach ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field

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

scholarly journals Signatures of Chaos in Nonintegrable Models of Quantum Field Theories

2021 ◽  
Vol 126 (12) ◽  
Author(s):  
Miha Srdinšek ◽  
Tomaž Prosen ◽  
Spyros Sotiriadis
Keyword(s):  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field

scholarly journals An algebraic criterion for the ultraviolet finiteness of quantum field theories

2001 ◽  
Vol 34 (44) ◽  
pp. 9485-9505 ◽  
Author(s):  
V E R Lemes ◽  
M S Sarandy ◽  
S P Sorella ◽  
O S Ventura ◽  
L C Q Vilar
Keyword(s):  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Algebraic Criterion
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