Bogolyubov transformation in the problem of capture of a massive particle by a quantum field

1980 ◽  
Vol 45 (3) ◽  
pp. 1069-1077
Author(s):  
Sh. I. Vashakidze ◽  
V. A. Matveev
Keyword(s):  
Massive Particle ◽  
Quantum Field ◽  
Bogolyubov Transformation

Quaternionic Dirac free particle

2021 ◽  
Author(s):  
Sergio Giardino
Keyword(s):  
Field Theory ◽  
Dirac Equation ◽  
Real Hilbert Space ◽  
Free Particle ◽  
Massive Particle ◽  
Essential Element ◽  
Massless Particle ◽  
Quantum Field ◽  
Quaternionic Quantum Mechanics ◽  
Theory Formula

In this paper, we solve the quaternionic Dirac equation [Formula: see text] in the real Hilbert space, and we ascertain that their free particle solutions set comprises eight elements in the case of a massive particle, and a four elements solutions set in the case of a massless particle, a richer situation when compared to the four elements solutions set of the usual complex Dirac equation [Formula: see text]. These free particle solutions were unknown in the previous solutions of anti-Hermitian quaternionic quantum mechanics, and constitute an essential element in order to build a quaternionic quantum field theory [Formula: see text].

scholarly journals Z0 →2γ AND THE TWISTED COPRODUCT OF THE POINCARÉ GROUP

2007 ◽  
Vol 22 (32) ◽  
pp. 6133-6146 ◽  
Author(s):  
A. P. BALACHANDRAN ◽  
S. G. JO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
General Result ◽  
Invariant Theory ◽  
Massive Particle ◽  
Lepton Number ◽  
Quantum Field ◽  
Poincaré Group ◽  
Poincare Group ◽  
Special Case

Yang's theorem forbids the process Z0 →2γ in any Poincaré invariant theory if photons are bosons and their two-particle states transform under the Poincaré group in the standard way (under the standard coproduct of the Poincaré group). This is an important result as it does not depend on the assumptions of quantum field theory. Recent work on noncommutative geometry requires deforming the above coproduct by the Drinfel'd twist. We prove that Z0 →2γ is forbidden for the twisted coproduct as well. This result is also independent of the assumptions of quantum field theory. As an illustration of the use of our general formulae, we further show that Z0 →ν+ ν is forbidden for the standard or twisted coproduct of the Poincaré group if the neutrino is massless, even if lepton number is violated. This is a special case of our general result that a massive particle of spin j cannot decay into two identical massless particles of the same helicity if j is odd, regardless of the coproduct used.

Relativistic Invariance and Mass Renormalization in Quantum Field Theory

2014 ◽  
Vol 59 (11) ◽  
pp. 1060-1064
Author(s):  
P.A. Frolov ◽  
◽  
A.V. Shebeko ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Relativistic Invariance ◽  
Mass Renormalization

A Review of Conformal Field Theory in 2D

2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Statistical Mechanics ◽  
Critical Behavior ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Quantum Field ◽  
Conformal Field ◽  
Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  

Some remarks on a deformed quantum field theory

2002 ◽  
Author(s):  
Marco Aurelio Do Rego Monteiro ◽  
V. B. Bezerra ◽  
E. M.F. Curado
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field

Global symmetries and Noether’s theorem

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Global Symmetries ◽  
Symmetry Transformation ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Quantum Field ◽  
Expectation Value ◽  
Minkowski Space Time ◽  
Integral Measure ◽  
Colour Charge ◽  
Internal Symmetries

Noethers theorem shows that continuous global symmetries lead classically to conservation laws. Such symmetries can be divided into spacetime and internal symmetries. The invariance of Minkowski space-time under global Poincaré transformations leads to the conservation of the four-momentum and the total angular momentum. Examples for conserved charges due to internal symmetries are electric and colour charge. The vacuum expectation value of a Noether current is shown to beconserved in a quantum field theory if the symmetry transformation keeps the path-integral measure invariant.

Quantum mechanics

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Transition Amplitude ◽  
External Source ◽  
Quantum Field ◽  
Damping Term ◽  
Relativistic Quantum Theory ◽  
Generating Functional

After a brief review of the operator approach to quantum mechanics, Feynmans path integral, which expresses a transition amplitude as a sum over all paths, is derived. Adding a linear coupling to an external source J and a damping term to the Lagrangian, the ground-state persistence amplitude is obtained. This quantity serves as the generating functional Z[J] for n-point Green functions which are the main target when studying quantum field theory. Then the harmonic oscillator as an example for a one-dimensional quantum field theory is discussed and the reason why a relativistic quantum theory should be based on quantum fields is explained.

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