Quantum Fields

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Field Theory ◽  
Topological Defects ◽  
Research Literature ◽  
Integral Approach ◽  
Quantum Field ◽  
Yang Mills ◽  
Gravitational Fields ◽  
Massless Spin ◽  
The Stability ◽  
Effective Theories

This book introduces quantum field theory, together with its most important applications to cosmology and astroparticle physics, in a coherent framework. The path-integral approach is employed right from the start, and the use of Green functions and generating functionals is illustrated first in quantum mechanics and then in scalar field theory. Massless spin one and two fields are discussed on an equal footing, and gravity is presented as a gauge theory in close analogy with the Yang–Mills case. Concepts relevant to modern research such as helicity methods, effective theories, decoupling, or the stability of the electroweak vacuum are introduced. Various applications such as topological defects, dark matter, baryogenesis, processes in external gravitational fields, inflation and black holes help students to bridge the gap between undergraduate courses and the research literature.

scholarly journals Trace dynamics and division algebras: towards quantum gravity and unification

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Tejinder P. Singh
Keyword(s):  
Lie Group ◽  
Planck Scale ◽  
The Self ◽  
Division Algebras ◽  
Quantum Field ◽  
Octonion Algebra ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Massless Spin ◽  
Correct Understanding

AbstractWe have recently proposed a Lagrangian in trace dynamics at the Planck scale, for unification of gravitation, Yang–Mills fields, and fermions. Dynamical variables are described by odd-grade (fermionic) and even-grade (bosonic) Grassmann matrices. Evolution takes place in Connes time. At energies much lower than Planck scale, trace dynamics reduces to quantum field theory. In the present paper, we explain that the correct understanding of spin requires us to formulate the theory in 8-D octonionic space. The automorphisms of the octonion algebra, which belong to the smallest exceptional Lie group G2, replace space-time diffeomorphisms and internal gauge transformations, bringing them under a common unified fold. Building on earlier work by other researchers on division algebras, we propose the Lorentz-weak unification at the Planck scale, the symmetry group being the stabiliser group of the quaternions inside the octonions. This is one of the two maximal sub-groups of G2, the other one being SU(3), the element preserver group of octonions. This latter group, coupled with U(1)em, describes the electrocolour symmetry, as shown earlier by Furey. We predict a new massless spin one boson (the ‘Lorentz’ boson) which should be looked for in experiments. Our Lagrangian correctly describes three fermion generations, through three copies of the group G2, embedded in the exceptional Lie group F4. This is the unification group for the four fundamental interactions, and it also happens to be the automorphism group of the exceptional Jordan algebra. Gravitation is shown to be an emergent classical phenomenon. Although at the Planck scale, there is present a quantised version of the Lorentz symmetry, mediated by the Lorentz boson, we argue that at sub-Planck scales, the self-adjoint part of the octonionic trace dynamics bears a relationship with string theory in 11 dimensions.

scholarly journals ON THE QUANTUM THEORY OF MASSLESS SPIN-3/2 FIELD IN MINKOWSKI SPACETIME

2006 ◽  
Vol 03 (07) ◽  
pp. 1303-1312 ◽  
Author(s):  
WEIGANG QIU ◽  
FEI SUN ◽  
HONGBAO ZHANG
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Casimir Effect ◽  
Minkowski Spacetime ◽  
Quantum Field ◽  
Explicit Result ◽  
Massless Spin ◽  
The Many ◽  
The One

From the modern viewpoint and by the geometric method, this paper provides a concise foundation for the quantum theory of massless spin-3/2 field in Minkowski spacetime, which includes both the one-particle's quantum mechanics and the many-particle's quantum field theory. The explicit result presented here is useful for the investigation of spin-3/2 field in various circumstances such as supergravity, twistor programme, Casimir effect, and quantum inequality.

scholarly journals Diluted mass gap in strongly coupled non-local Yang-Mills

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Marco Frasca ◽  
Anish Ghoshal
Keyword(s):  
Field Theory ◽  
Particle Physics ◽  
Mass Scale ◽  
Local Theory ◽  
Quantum Field ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Mass Gap ◽  
Non Local ◽  
Non Locality

Abstract We investigate the non-perturbative regimes in the class of non-Abelian theories that have been proposed as an ultraviolet completion of 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite series of higher-order derivatives inspired by string field theory. We prove that, at the non-perturbative level, the physical spectrum of the theory is actually corrected by the “infinite number of derivatives” present in the action. We derive a set of Dyson-Schwinger equations in differential form, for correlation functions till two-points, the solution for which are known in the local theory. We obtain that just like in the local theory, the non-local counterpart displays a mass gap, depending also on the mass scale of non-locality, and show that it is damped in the deep UV asymptotically. We point out some possible implications of our result in particle physics and cosmology and discuss aspects of non-local QCD-like scenarios.

scholarly journals Some comments on infinities on quantum field theory: A functional integral approach

2016 ◽  
Vol 24 (2) ◽  
Author(s):  
Luiz C. L. Botelho
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Function Space ◽  
Functional Integral ◽  
Field Theories ◽  
Integral Approach ◽  
Quantum Field ◽  
Functional Integrals ◽  
Euclidean Field ◽  
The Subject

AbstractWe analyze on the formalism of probabilities measures-functional integrals on function space the problem of infinities on Euclidean field theories. We also clarify and generalize our previous published studies on the subject.

scholarly journals DIFFERENTIAL GEOMETRY FROM QUANTUM FIELD THEORY

2013 ◽  
Vol 10 (04) ◽  
pp. 1350003
Author(s):  
W. F. CHEN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Differential Geometry ◽  
Historical Development ◽  
Theoretical Physics ◽  
Quantum Field ◽  
Yang Mills ◽  
And Mathematics

We review the historical development and physical ideas of topological Yang–Mills theory and explain how quantum field theory, a physical framework describing subatomic physics, can be used as a tool to study differential geometry. We further emphasize that this phenomenon demonstrates that the inter-relation between theoretical physics and mathematics have come into a new stage.

scholarly journals Broken Symmetry and Yang–Mills Theory

2014 ◽  
Vol 03 (01) ◽  
pp. 54-67 ◽  
Author(s):  
François Englert
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Statistical Physics ◽  
Broken Symmetry ◽  
Quantum Field ◽  
Yang Mills

From its inception in statistical physics to its role in the construction and in the development of the asymmetric Yang–Mills phase in quantum field theory, the notion of spontaneous broken symmetry permeates contemporary physics. This is reviewed with particular emphasis on the conceptual issues.

THE FIRST DONALDSON INVARIANT AS THE WINDING NUMBER OF A NICOLAI MAP

1988 ◽  
Vol 03 (17) ◽  
pp. 1647-1650 ◽  
Author(s):  
P. MANSFIELD
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Partition Function ◽  
Relativistic Quantum ◽  
Quantum Field ◽  
Winding Number ◽  
Relativistic Quantum Field Theory ◽  
Yang Mills ◽  
Stochastic Map

We show that the first Donaldson invariant expressed by Witten as the partition function of a relativistic quantum field theory can be interpreted as the winding number of the stochastic map introduced by Nicolai in the context of supersymmetric Yang-Mills theories.

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