scholarly journals Lie Group Classification of Generalized Variable Coefficient Korteweg-de Vries Equation with Dual Power-Law Nonlinearities with Linear Damping and Dispersion in Quantum Field Theory

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 83
Author(s):  
Oke Davies Adeyemo ◽  
Chaudry Masood Khalique
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Power Law ◽  
Lie Group ◽  
Variable Coefficient ◽  
Variable Coefficients ◽  
Group Classification ◽  
Quantum Field ◽  
Lie Group Classification

Many physical phenomena in fields of studies such as optical fibre, solid-state physics, quantum field theory and so on are represented using nonlinear evolution equations with variable coefficients due to the fact that the majority of nonlinear conditions involve variable coefficients. In consequence, this article presents a complete Lie group analysis of a generalized variable coefficient damped wave equation in quantum field theory with time-dependent coefficients having dual power-law nonlinearities. Lie group classification of two distinct cases of the equation was performed to obtain its kernel algebra. Thereafter, symmetry reductions and invariant solutions of the equation were obtained. We also investigate various soliton solutions and their dynamical wave behaviours. Further, each class of general solutions found is invoked to construct conserved quantities for the equation with damping term via direct technique and homotopy formula. In addition, Noether’s theorem is engaged to furnish more conserved currents of the equation under some classifications.

Lie group classification of the N-th-order nonlinear evolution equations

2011 ◽  
Vol 54 (12) ◽  
pp. 2553-2572 ◽  
Author(s):  
ShouFeng Shen ◽  
ChangZheng Qu ◽  
Qing Huang ◽  
YongYang Jin
Keyword(s):  
Lie Group ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Group Classification ◽  
Nonlinear Evolution Equations ◽  
Lie Group Classification

Lie group classification of second-order ordinary difference equations

2000 ◽  
Vol 41 (1) ◽  
pp. 480-504 ◽  
Author(s):  
Vladimir Dorodnitsyn ◽  
Roman Kozlov ◽  
Pavel Winternitz
Keyword(s):  
Lie Group ◽  
Difference Equations ◽  
Group Classification ◽  
Second Order ◽  
Lie Group Classification

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 Quantum quench and thermalization to GGE in arbitrary dimensions and the odd-even effect

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Parijat Banerjee ◽  
Adwait Gaikwad ◽  
Anurag Kaushal ◽  
Gautam Mandal
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Power Law ◽  
Cold Atom ◽  
Quantum Field ◽  
Approach To Equilibrium ◽  
Zero Mass ◽  
Quantum Quench ◽  
Spatial Dimensions ◽  
Arbitrary Dimensions

Abstract In many quantum quench experiments involving cold atom systems the post-quench phase can be described by a quantum field theory of free scalars or fermions, typically in a box or in an external potential. We will study mass quench of free scalars in arbitrary spatial dimensions d with particular emphasis on the rate of relaxation to equilibrium. Local correlators expectedly equilibrate to GGE; for quench to zero mass, interestingly the rate of approach to equilibrium is exponential or power law depending on whether d is odd or even respectively. For quench to non-zero mass, the correlators relax to equilibrium by a cosine-modulated power law, for all spatial dimensions d, even or odd. We briefly discuss generalization to O(N ) models.

HAAG DUALITY IN CONFORMAL QUANTUM FIELD THEORY

1990 ◽  
Vol 02 (01) ◽  
pp. 105-125 ◽  
Author(s):  
DETLEV BUCHHOLZ ◽  
HANNS SCHULZ-MIRBACH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Central Charge ◽  
Algebraic Approach ◽  
Energy Tensor ◽  
Quantum Field ◽  
Haag Duality ◽  
Conformal Fields ◽  
Stress Energy

Haag duality is established in conformal quantum field theory for observable fields on the compactified light ray S1 and Minkowski space S1×S1, respectively. This result provides the foundation for an algebraic approach to the classification of conformal theories. Haag duality can fail, however, for the restriction of conformal fields to the underlying non-compact spaces ℝ, respectively ℝ×ℝ. A prominent example is the stress energy tensor with central charge c>1.

scholarly journals TOWARDS A CLASSIFICATION OF FINITE FIELD THEORIES

1994 ◽  
Vol 09 (27) ◽  
pp. 2555-2567
Author(s):  
PETER GRANDITS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Finite Field ◽  
Field Theories ◽  
Quantum Field ◽  
Particle Content ◽  
Finiteness Conditions ◽  
Gauge Groups ◽  
Yukawa Couplings

We consider the finiteness conditions on the Yukawa couplings of a general quantum field theory for gauge groups SU (n)(n>6) and a rather general particle content. It is shown that in the class of theories considered (149 different particle contents), only two models are able to fulfill the finiteness conditions. Only one of these is supersymmetric. For the nonsupersymmetric one the appropriate Yukawa couplings are constructed explicitly.

scholarly journals Lie group classification of first-order delay ordinary differential equations

2018 ◽  
Vol 51 (20) ◽  
pp. 205202 ◽  
Author(s):  
Vladimir A Dorodnitsyn ◽  
Roman Kozlov ◽  
Sergey V Meleshko ◽  
Pavel Winternitz
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Lie Group ◽  
Group Classification ◽  
First Order ◽  
Lie Group Classification

scholarly journals CHERN–SIMONS APPROACH TO THREE-MANIFOLD INVARIANTS

1995 ◽  
Vol 10 (06) ◽  
pp. 487-493
Author(s):  
BOGUSŁAW BRODA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Lie Group ◽  
Three Dimensional ◽  
Simons Theory ◽  
Quantum Field ◽  
Topological Quantum ◽  
Chern Simons ◽  
Direct Implementation ◽  
Chern Simons Theory

A new, formal, noncombinatorial approach to invariants of three-dimensional manifolds of Reshetikhin, Turaev and Witten in the framework of nonperturbative topological quantum Chern–Simons theory, corresponding to an arbitrary compact simple Lie group, is presented. A direct implementation of surgery instructions in the context of quantum field theory is proposed. An explicit form of the specialization of the invariant to the group SU(2) is shown.

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