Gauge Field Theory in Natural Geometric Language

2020 ◽  
Author(s):  
Daniel Canarutto
Keyword(s):  
Particle Physics ◽  
Quantum Physics ◽  
Brst Symmetry ◽  
Natural Extension ◽  
Integrated Approach ◽  
Arbitrary Spin ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Standard View ◽  
Spinor Bundle

This monograph addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a not-too-short, integrated approach that exploits standard and non-standard notions in natural geometric language. The role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. Two-spinors yield a partly original ‘minimal geometric data’ approach to Einstein-Cartan-Maxwell-Dirac fields. The gravitational field is jointly represented by a spinor connection and by a soldering form (a ‘tetrad’) valued in a vector bundle naturally constructed from the assumed 2-spinor bundle. We give a presentation of electroweak theory that dispenses with group-related notions, and we introduce a non-standard, natural extension of it. Also within the 2-spinor approach we present: a non-standard view of gauge freedom; a first-order Lagrangian theory of fields with arbitrary spin; an original treatment of Lie derivatives of spinors and spinor connections. Furthermore we introduce an original formulation of Lagrangian field theories based on covariant differentials, which works in the classical and quantum field theories alike and simplifies calculations. We offer a precise mathematical approach to quantum bundles and quantum fields, including ghosts, BRST symmetry and anti-fields, treating the geometry of quantum bundles and their jet prolongations in terms Frölicher's notion of smoothness. We propose an approach to quantum particle physics based on the notion of detector, and illustrate the basic scattering computations in that context.

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 From QFT to 2-d Supersymetric TQT:Mirror symmetry between Math and Physic

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Mirror Symmetry ◽  
Quantum Physics ◽  
Geometric Approach ◽  
Theoretical Physics ◽  
Field Theories ◽  
Quantum Field Theories ◽  
And Topology ◽  
Topological Field ◽  
Topological Theories ◽  
The Universe

Theoretical physics is taking an increasing part in the universe of mathematics. After calculus, vector and tensorial analysis, topological theories make their entry into quantum field theories. More precisely, in this domain, topological theories are the most relevant. A fundamental theorem of the Atiyah has important repercussions in several branches of quantum physics in the geometric approach. We can cite the work of Alain Connes on non-commutative geometry, but also all the developments due to Donaldson, E. Witten around Gauge theories, superstring and Mirror Symmetry. We present here an historical survey of some topological field theories, especially Mirror Symmetry to understand the interpenetration between quantum physics and topology.

scholarly journals LIFSHITZ-TYPE QUANTUM FIELD THEORIES IN PARTICLE PHYSICS

2011 ◽  
Vol 26 (26) ◽  
pp. 4523-4541 ◽  
Author(s):  
JEAN ALEXANDRE
Keyword(s):  
Particle Physics ◽  
Lorentz Symmetry ◽  
The Other ◽  
Field Theories ◽  
Asymptotic Freedom ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Mass Generation ◽  
Dynamical Mass ◽  
Other Hand

This introduction to Lifshitz-type field theories reviews some of its aspects in Particle Physics. Attractive features of these models are described with different examples, as the improvement of graphs convergence, the introduction of new renormalizable interactions, dynamical mass generation, asymptotic freedom, and other features related to more specific models. On the other hand, problems with the expected emergence of Lorentz symmetry in the IR are discussed, related to the different effective light cones seen by different particles when they interact.

A few solvable two-dimensional quantum field theories (QFT)

2021 ◽  
pp. 721-746
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Chiral Symmetry Breaking ◽  
Spin Model ◽  
Two Dimensions ◽  
Thirring Model ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Two Dimensional

The chapter is devoted to several two-dimensional quantum field theories (QFT), whose properties can be determined by non-perturbative methods. The Schwinger model, a model of two-dimensional quantum electrodynamics (QED) with massless fermions, illustrates the properties of confinement, spontaneous chiral symmetry breaking, asymptotic freedom and anomalies, properties one also expects in particle physics from quantum chromodynamics. The equivalence between the massive Thirring model, a fermion model with current–current interaction, and the sine-Gordon model is derived, using the bozonisation technique. The bosonization technique, based on an identity for Cauchy determinants, establishes relations, specific to two dimensions, between fermion and boson local field theories. Several generalized Thirring model are also discussed. In the discussion of the O(N) non-linear σ-model, it has been noticed that the Abelian case N = 2 is special, because the renormalization group (RG) β-function vanishes in two dimensions. The corresponding O(2) invariant spin model is especially interesting: it provides an example of the celebrated Kosterlitz–Thouless (KT) phase transition and will be studied elsewhere. This chapter also provides the necessary technical background for such an investigation.

Approaches to the sign problem in lattice field theory

2016 ◽  
Vol 31 (22) ◽  
pp. 1643007 ◽  
Author(s):  
Christof Gattringer ◽  
Kurt Langfeld
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Particle Physics ◽  
Field Theories ◽  
Quantum Field Theories ◽  
First Principle ◽  
Quantum Field ◽  
Complex Action ◽  
Lattice Field ◽  
Sign Problem

Quantum field theories (QFTs) at finite densities of matter generically involve complex actions. Standard Monte Carlo simulations based upon importance sampling, which have been producing quantitative first principle results in particle physics for almost forty years, cannot be applied in this case. Various strategies to overcome this so-called sign problem or complex action problem were proposed during the last thirty years. We here review the sign problem in lattice field theories, focusing on two more recent methods: dualization to worldline type of representations and the density-of-states approach.

BRST FIELD THEORIES FOR A QUANTUM LORENTZ PARTICLE

1992 ◽  
Vol 07 (06) ◽  
pp. 1187-1213 ◽  
Author(s):  
MACHIKO HATSUDA
Keyword(s):  
Field Theory ◽  
Brst Symmetry ◽  
Arbitrary Spin ◽  
Field Theories ◽  
Gauge Fields ◽  
Field Equations ◽  
Tensor Fields ◽  
Guiding Principle ◽  
Brst Charge ◽  
Brst Cohomology

From the study of string field theory, first quantized BRST symmetry is known to be a guiding principle in constructing field theories. We construct the first quantized BRST charge QB for a quantum Lorentz particle which is characterized by the constraints which are expressed in terms of (inhomogeneous) Lorentz generators. It is shown that the BRST cohomology of this system includes only the field strengths and not the fundamental gauge fields with nontrivial norms. By using this BRST charge, we obtain the field theory Lagrangian via the ∫ΨQBΨ construction, which leads to field equations for fields with arbitrary spin. However, this action cannot be used to derive a second quantized theory except for Dirac fields. For antisymmetric tensor fields, we can get the correct second quantized theories if we introduce extra conditions.

scholarly journals REFLECTIONS ON THE SPATIOTEMPORAL ASPECTS OF THE QUANTUM WORLD

2002 ◽  
Vol 17 (15n17) ◽  
pp. 1107-1121 ◽  
Author(s):  
ULRICH MOHRHOFF
Keyword(s):  
Particle Physics ◽  
Measurement Problem ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Top Down ◽  
Fuzzy Variables ◽  
Quantum Gravity Phenomenology ◽  
Physical Consequences ◽  
Proper Resolution

The proper resolution of the so-called measurement problem requires a "top-down" conception of the quantum world that is opposed to the usual "bottom-up" conception, which builds on an intrinsically and maximally differentiated manifold. The key to that problem is that the fuzziness of a variable can manifest itself only to the extent that less fuzzy variables exist. Inasmuch as there is nothing less fuzzy than the metric, this argues against a quantum-gravity phenomenology and suggests that a quantum theory of gravity is something of a contradiction in terms — a theory that would make it possible to investigate the physics on scales that do not exist, or to study the physical consequences of a fuzziness that has no physical consequences, other than providing a natural cutoff for the quantum field theories of particle physics.

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