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.

CONSTRUCTING TQFTS FROM MODULAR FUNCTORS

2001 ◽  
Vol 10 (08) ◽  
pp. 1085-1131 ◽  
Author(s):  
JAKOB GROVE
Keyword(s):  
The Other ◽  
Field Theories ◽  
Careful Study ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Other Hand ◽  
Topological Quantum ◽  
Extended Surfaces ◽  
Modular Functor ◽  
Marked Points

We prove in this paper that any 2 dimensional modular functor satisfying that S1,1≠0 induces a family of 2+1 dimensionally topological quantum field theories. We do this for two kinds of modular functors namely a modular functor on the category of extended surfaces and a modular functor on the category of extended surfaces with marked points and directions. We follow the ideas of M. Kontsevich, [21], and K. Walker, [32] but we give proofs and provide details left out in [21] and [32]. Careful study also shows that more choices are needed to define the TQFT than it is revealed in [21] and [32]. On the other hand, relations found in [32] turns out not to be needed here.

scholarly journals Quantum Field Theory over $\mathbb{F}_q$

10.37236/589 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Oliver Schnetz
Keyword(s):  
Field Theory ◽  
Perturbation Series ◽  
The Other ◽  
Field Theories ◽  
Roots Of Unity ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Feynman Rules ◽  
Graph Hypersurfaces ◽  
Prime 2

We consider the number $\bar N(q)$ of points in the projective complement of graph hypersurfaces over $\mathbb{F}_q$ and show that the smallest graphs with non-polynomial $\bar N(q)$ have 14 edges. We give six examples which fall into two classes. One class has an exceptional prime 2 whereas in the other class $\bar N(q)$ depends on the number of cube roots of unity in $\mathbb{F}_q$. At graphs with 16 edges we find examples where $\bar N(q)$ is given by a polynomial in $q$ plus $q^2$ times the number of points in the projective complement of a singular K3 in $\mathbb{P}^3$. In the second part of the paper we show that applying momentum space Feynman-rules over $\mathbb{F}_q$ lets the perturbation series terminate for renormalizable and non-renormalizable bosonic quantum field theories.

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

The Principles of Renormalisation

2021 ◽  
pp. 304-328
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Expansion ◽  
Power Counting ◽  
Field Theories ◽  
Asymptotic Freedom ◽  
Green Functions ◽  
Quantum Field Theories ◽  
Quantum Field

Loop diagrams often yield ultraviolet divergent integrals. We introduce the concept of one-particle irreducible diagrams and develop the power counting argument which makes possible the classification of quantum field theories into non-renormalisable, renormalisable and super-renormalisable. We describe some regularisation schemes with particular emphasis on dimensional regularisation. The renormalisation programme is described at one loop order for φ‎4 and QED. We argue, without presenting the detailed proof, that the programme can be extended to any finite order in the perturbation expansion for every renormalisable (or super-renormalisable) quantum field theory. We derive the equation of the renormalisation group and explain how it can be used in order to study the asymptotic behaviour of Green functions. This makes it possible to introduce the concept of asymptotic freedom.

scholarly journals SUBFACTORS AND 1+1-DIMENSIONAL TQFTs

2007 ◽  
Vol 18 (01) ◽  
pp. 69-112 ◽  
Author(s):  
VIJAY KODIYALAM ◽  
VISHWAMBHAR PATI ◽  
V. S. SUNDER
Keyword(s):  
The Other ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Planar Algebras ◽  
Topological Quantum ◽  
The One ◽  
Topological Quantum Field Theories

We construct a certain "cobordism category" [Formula: see text] whose morphisms are suitably decorated cobordism classes between similarly decorated closed oriented 1-manifolds, and show that there is essentially a bijection between (1+1-dimensional) unitary topological quantum field theories (TQFTs) defined on [Formula: see text], on the one hand, and Jones' subfactor planar algebras, on the other.

scholarly journals IN–IN FORMALISM, PSEUDO-INSTANTONS AND RETHINKING QUANTUM COSMOLOGY

2014 ◽  
Vol 23 (03) ◽  
pp. 1450026 ◽  
Author(s):  
ALI KAYA
Keyword(s):  
Path Integral ◽  
Quantum Cosmology ◽  
Flat Space ◽  
The Other ◽  
Field Theories ◽  
Asymptotic Region ◽  
Quantum Field Theories ◽  
Infinite Volume ◽  
Quantum Field ◽  
Integral Measure

Unlike flat space quantum field theories that focus on scattering amplitudes, the main observables in quantum cosmology are correlation functions. The systematic way of calculating correlators is called in–in formalism, which requires only a single asymptotic region, i.e. past infinity. The rules in perturbation theory and the path integral measure are very different for in–in and in–out formalisms, and thus the results which are standard in one approach may not necessarily hold in the other one. We show that stationary phase approximation works completely different for a scalar in–in path integral. Hence, in a cosmological background there are solutions, pseudo-instantons, that allow tunneling between locally stable vacua even in infinite volume, which is counterintuitive from an in–out perspective. We argue that various familiar notions of in–out formalism must be re-examined in the in–in formalism, which might have important consequences for quantum cosmology.

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.

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