Pair creation of neutral Dirac particle in (1 + 2)d noncommutative spacetime

2018 ◽  
Vol 33 (03) ◽  
pp. 1850017 ◽  
Author(s):  
B. Hamil
Keyword(s):  
Neutral Particle ◽  
Pair Creation ◽  
Dirac Particle ◽  
Bogoliubov Transformation ◽  
Quantum Fields ◽  
Field Equations ◽  
First Order ◽  
Noncommutative Spacetime

In this paper, we study the influence of the noncommutativity on the pairs creation of neutral particle–antiparticle in (1 + 2)d. Using the Seiberg–Witten maps, the modified Euler–Lagrange field equations up to first-order in the noncommutativity, parameter [Formula: see text] is obtained and the Nikishov method based on Bogoliubov transformation is applied to calculate the density number of created neutral fermions. It is shown that the noncommutativity amplifies the density number N. In addition, when [Formula: see text], we obtain the known results corresponding to the undeformed quantum fields.

scholarly journals The Particle as a Statistical Ensemble of Events in Stueckelberg-Horwitz-Piron Electrodynamics †

2017 ◽  
Author(s):  
Martin Land
Keyword(s):  
Time Reversal ◽  
Lorentz Invariance ◽  
Pair Creation ◽  
Statistical Ensemble ◽  
Field Equations ◽  
Maxwell Theory ◽  
Classical Level ◽  
Equilibrium Limit ◽  
First Order ◽  
A Current

Stueckelberg-Horwitz-Piron (SHP) electrodynamics formalizes the distinction between coordinate time (measured by laboratory clocks) and chronology (temporal ordering) by defining 4D spacetime events xμ as functions of an external evolution parameter τ. Classical spacetime events xμ (τ) evolve as τ grows monotonically, tracing out particle worldlines dynamically and inducing the five U(1) gauge potentials through which events interact. Since Lorentz invariance imposes time reversal symmetry on x0 but not τ, the formalism resolves grandfather paradoxes and related problems of irreversibility. The action involves standard first order field derivatives but includes a higher order τ derivative that while preserving gauge and Lorentz invariance removes certain singularities and makes the related QFT super-renormalizable. The resulting field equations are Maxwell-like but τ-dependent and sourced by a current that represents a statistical ensemble of instantaneous events distributed along the worldline. The width λ of this distribution defines a correlation time for the interactions and a mass spectrum for the photons that carry the interaction. As λ becomes very large, the photon mass goes to zero and the field equations become τ-independent Maxwell’s equations. Maxwell theory thus emerges as an equilibrium limit of SHP, in which λ is larger than any other relevant time scale. Particles and fields are not constrained to mass shells in SHP theory, and by exchanging mass may produce pair creation/annihilation processes at the classical level. On-shell evolution with fixed particle masses is restored through a self-interaction associated with the 5D wave equation.

Geometric quantization and the Bogoliubov transformation

1981 ◽  
Vol 378 (1772) ◽  
pp. 119-139 ◽  
Keyword(s):  
Phase Space ◽  
Geometric Quantization ◽  
Classical Field ◽  
Bogoliubov Transformation ◽  
Quantum Fields ◽  
Boson Field ◽  
Field Equations ◽  
Functional Integrals ◽  
Fermion Fields ◽  
Classical Phase Space

This paper treats some simple applications of geometric quantization theory to problems involving the interaction of quantum fields with ex­ternal classical potentials. The main new result is a representation of the transition amplitudes for a boson field in terms of functional integrals over the classical phase space (the space of solutions of the classical field equations). An analogous representation for fermion fields is also con­structed.

On Conformally Covariant Spinor Field Equations

1972 ◽  
Vol 50 (18) ◽  
pp. 2100-2104 ◽  
Author(s):  
Mark S. Drew
Keyword(s):  
Minkowski Space ◽  
Invariant Mass ◽  
Spinor Field ◽  
Dimensional Space ◽  
Flat Space ◽  
Field Equations ◽  
First Order ◽  
Conformally Invariant ◽  
Spinor Fields

Conformally covariant equations for free spinor fields are determined uniquely by carrying out a descent to Minkowski space from the most general first-order rotationally covariant spinor equations in a six-dimensional flat space. It is found that the introduction of the concept of the "conformally invariant mass" is not possible for spinor fields even if the fields are defined not only on the null hyperquadric but over the entire manifold of coordinates in six-dimensional space.

scholarly journals ON THE CREATION OF SCALAR PARTICLES IN A FLAT ROBERTSON–WALKER SPACETIME

2011 ◽  
Vol 26 (35) ◽  
pp. 2639-2651 ◽  
Author(s):  
S. HAOUAT ◽  
R. CHEKIREB
Keyword(s):  
Exact Solutions ◽  
Effective Action ◽  
Gordon Equation ◽  
Transition Probability ◽  
Particle Creation ◽  
Pair Creation ◽  
Bogoliubov Transformation ◽  
Scalar Particles ◽  
Klein Gordon ◽  
Klein Gordon Equation

The problem of particle creation from vacuum in a flat Robertson–Walker spacetime is studied. Two sets of exact solutions for the Klein–Gordon equation are given when the scale factor is a2(η) = a+b tanh(λη)+c tanh2 (λη). Then the canonical method based on Bogoliubov transformation is applied to calculate the pair creation probability and the density number of created particles. Some particular cosmological models such as radiation dominated universe and Milne universe are discussed. For both cases the vacuum to vacuum transition probability is calculated and the imaginary part of the effective action is extracted.

Strength of the Poincaré gauge field equations in first order formalism

1989 ◽  
Vol 139 (1-2) ◽  
pp. 21-26 ◽  
Author(s):  
Michael Sué ◽  
Eckehard W. Mielke
Keyword(s):  
Gauge Field ◽  
Field Equations ◽  
First Order

WEAK SOLUTIONS FOR WEAK SINGULARITIES

2002 ◽  
Vol 17 (20) ◽  
pp. 2769-2769
Author(s):  
B. C. NOLAN
Keyword(s):  
Existence And Uniqueness ◽  
Finite Measure ◽  
Generalized Solutions ◽  
Functions Of Bounded Variation ◽  
Field Equations ◽  
Finite Radius ◽  
Locally Finite ◽  
Naked Singularities ◽  
First Order ◽  
Bounded Functions

We revisit the problem of the development of singularities in the gravitational collapse of an inhomogeneous dust sphere. As shown by Yodzis et al1, naked singularities may occur at finite radius where shells of dust cross one another. These singularities are gravitationally weak 2, and it has been claimed that at these singularities, the metric may be written in continuous form 2, with locally L∞ connection coefficients 3. We correct these claims, and show how the field equations may be reformulated as a first order, quasi-linear, non-conservative, non-strictly hyperbolic system. We discuss existence and uniqueness of generalized solutions of this system using bounded functions of bounded variation (BV) 4, where the product of a BV function and the derivative of another BV function may be interpreted as a locally finite measure. The solutions obtained provide a dynamical extension to the future of the singularity.

scholarly journals On GLM curl cleaning for a first order reduction of the CCZ4 formulation of the Einstein field equations

2020 ◽  
Vol 404 ◽  
pp. 109088 ◽  
Author(s):  
Michael Dumbser ◽  
Francesco Fambri ◽  
Elena Gaburro ◽  
Anne Reinarz
Keyword(s):  
Order Reduction ◽  
Einstein Field Equations ◽  
Field Equations ◽  
First Order
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