scholarly journals MASSLESS FIELDS OVER R1×H3 SPACE–TIME AND COHERENT STATES FOR THE LORENTZ GROUP

1999 ◽  
Vol 14 (30) ◽  
pp. 2119-2124 ◽  
Author(s):  
S. A. POL'SHIN
Keyword(s):  
Explicit Form ◽  
Lorentz Group ◽  
Coherent States ◽  
Wave Equations ◽  
Arbitrary Spin ◽  
Space Time ◽  
Generalized Coherent States ◽  
Massless Fields

The solutions of the arbitrary-spin massless wave equations over R1×H3 space are obtained using the generalized coherent states for the Lorentz group. The use of these solutions for the construction of invariant propagators of quantized massless fields with an arbitrary spin over the R1×H3 space is considered. The expression for the scalar propagator is obtained in the explicit form.

Multiphoton Laguerre polynomial state as minimum uncertainty states of intensity-dependent squeezing

2014 ◽  
Vol 92 (9) ◽  
pp. 1016-1020
Author(s):  
Qian-Fan Chen ◽  
Hong-Yi Fan
Keyword(s):  
Coherent State ◽  
Lie Algebra ◽  
Explicit Form ◽  
Coherent States ◽  
Fock Space ◽  
Laguerre Polynomial ◽  
Annihilation Operator ◽  
Nonlinear Realization ◽  
Generalized Coherent States ◽  
Minimum Uncertainty

For a general multiphoton annihilation operator, F = f(N)ap, where N = a†a, we find the explicit form of an operator, G†, which satisfies [F, G†] = 1. Based on the nonlinear realization of the SU(1,1) Lie algebra whose generators are [Formula: see text], [Formula: see text], and R0 = [N/p] + 1/2. We introduce the concept of intensity-dependent multiphoton squeezing and find that the state Lm(–yR†)|j⟩, 0 ≤ j ≤ p, where Lm(x) is a Laguerre polynomial, is a minimum uncertainty state for intensity-dependent multiphoton squeezing. We also construct the phase states for multiphoton operator, which turn out to be SU(1,1) generalized coherent states. Additionally, we show that the photon-added coherent state |α, m⟩ (m is a non-negative integer), which can be interpreted as a nonlinear coherent state, can be expressed as [Formula: see text] in the whole Fock space.

scholarly journals Coherent states, vacuum structure and infinite component relativistic wave equations

2016 ◽  
Vol 13 (01) ◽  
pp. 1650004 ◽  
Author(s):  
Diego Julio Cirilo-Lombardo
Keyword(s):  
Lorentz Group ◽  
Coherent States ◽  
Wave Equations ◽  
Recent Literature ◽  
Group Structure ◽  
Nucl Phys ◽  
Internal Variables ◽  
Positive Energy ◽  
Relativistic Wave ◽  
Infinite Component

It is commonly claimed in the recent literature that certain solutions to wave equations of positive energy of Dirac-type with internal variables are characterized by a non-thermal spectrum. As part of that statement, it was said that the transformations and symmetries involved in equations of such type corresponded to a particular representation of the Lorentz group. In this paper, we give the general solution to this problem emphasizing the interplay between the group structure, the corresponding algebra and the physical spectrum. This analysis is completed with a strong discussion and proving that: (i) the physical states are represented by coherent states; (ii) the solutions in [Yu. P. Stepanovsky, Nucl. Phys. B (Proc. Suppl.) 102 (2001) 407–411; 103 (2001) 407–411] are not general, (iii) the symmetries of the considered physical system in [Yu. P. Stepanovsky, Nucl. Phys. B (Proc. Suppl.) 102 (2001) 407–411; 103 (2001) 407–411] (equations and geometry) do not correspond to the Lorentz group but to the fourth covering: the Metaplectic group [Formula: see text].

VACUUM-VACUUM AMPLITUDES IN THE THEORY OF QUANTUM RADIATION BY MIRRORS IN 1+1-SPACE AND CHARGES IN 3+1-SPACE

2002 ◽  
Vol 17 (06n07) ◽  
pp. 1033-1040 ◽  
Author(s):  
VLADIMIR I. RITUS
Keyword(s):  
Lorentz Group ◽  
Wave Equations ◽  
Integral Relation ◽  
Space Time ◽  
The Self ◽  
Singular Solutions ◽  
Single Photons ◽  
Scalar Charge ◽  
Group Spin ◽  
Quantum Radiation

The symmetry between the creation of pairs of massless bosons or fermions by accelerated mirror in 1+1 space and the emission of single photons or scalar quanta by electric or scalar charge in 3+1 space is deepened in this paper. The relation of Bogoliubov coefficients, describing the processes generated by the mirror, with Fourier's components of current or charge density leads to the coicidence of the spin of any disturbances bilinear in scalar or spinor field with the spin of quanta emitted by the electric or scalar charge. The mass and invariant momentum transfer of these disturbances are essential for the relation of Bogoliubov coefficients with invariant singular solutions and Green's functions of wave equations both for 1+1 and 3+1 spaces and especially for the integral relation (20) between these solutions. Namely the last relation leads to the coincidence of the self-action changes and vacuum-vacuum amplitudes for the accelerated mirror in two-dimentional space-time and charge in four-dimentional space-time. Thus, both invariants of the Lorentz group, spin and mass, perform intrinsic role in established symmetry.

scholarly journals Space-Time Coupling: Current Concept and Two Examples from Ultrafast Optics Studied Using Exact Solution of EM Equations

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 529
Author(s):  
Nikolay L. Popov ◽  
Alexander V. Vinogradov
Keyword(s):  
Wave Equations ◽  
Coherent Control ◽  
Ultrafast Optics ◽  
Spectral Width ◽  
Space Time ◽  
Current Approach ◽  
Unipolar Pulse ◽  
Number Of Cycles ◽  
Control Of Quantum Systems ◽  
Coupling Current

Current approach to space-time coupling (STC) phenomena is given together with a complementary version of the STC concept that emphasizes the finiteness of the energy of the considered pulses. Manifestations of STC are discussed in the framework of the simplest exact localized solution of Maxwell’s equations, exhibiting a “collapsing shell”. It falls onto the center, continuously deforming, and then, having reached maximum compression, expands back without losing energy. Analytical solutions describing this process enable to fully characterize the field in space-time. It allowed to express energy density in the center of collapse in the terms of total pulse energy, frequency and spectral width in the far zone. The change of the pulse shape while travelling from one point to another is important for coherent control of quantum systems. We considered the excitation of a two-level system located in the center of the collapsing EM (electromagnetic) pulse. The result is again expressed through the parameters of the incident pulse. This study showed that as it propagates, a unipolar pulse can turn into a bipolar one, and in the case of measuring the excitation efficiency, we can judge which of these two pulses we are dealing with. The obtained results have no limitation on the number of cycles in a pulse. Our work confirms the productivity of using exact solutions of EM wave equations for describing the phenomena associated with STC effects. This is facilitated by rapid progress in the search for new types of such solutions.

CRYSTALLINE GRAVITY

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3243-3255 ◽  
Author(s):  
GERARD 't HOOFT
Keyword(s):  
Finite Number ◽  
Lorentz Group ◽  
Degrees Of Freedom ◽  
Holonomy Group ◽  
Discrete Subgroup ◽  
Analytic Solutions ◽  
Space Time ◽  
Exact Analytic Solutions ◽  
Finite Domains ◽  
Dimensional Crystal

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate a theory that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Next, we suggest replacing in the string holonomy group, the Lorentz group by a discrete subgroup, which turns space-time into a 4-dimensional crystal with defects.

scholarly journals Global existence and decay estimates for nonlinear wave equations with space-time dependent dissipative term

2015 ◽  
Vol 12 (02) ◽  
pp. 249-276
Author(s):  
Tomonari Watanabe
Keyword(s):  
Global Existence ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Space Time ◽  
Time Dependent ◽  
Nonlinear Wave Equations ◽  
Energy Estimates ◽  
Space Region ◽  
Decay Estimates ◽  
Dissipative Term

We study the global existence and the derivation of decay estimates for nonlinear wave equations with a space-time dependent dissipative term posed in an exterior domain. The linear dissipative effect may vanish in a compact space region and, moreover, the nonlinear terms need not be in a divergence form. In order to establish higher-order energy estimates, we introduce an argument based on a suitable rescaling. The proposed method is useful to control certain derivatives of the dissipation coefficient.

scholarly journals POLYHOMOGENEOUS SOLUTIONS OF NONLINEAR WAVE EQUATIONS WITHOUT CORNER CONDITIONS

2006 ◽  
Vol 03 (01) ◽  
pp. 81-141 ◽  
Author(s):  
PIOTR T. CHRUŚCIEL ◽  
SZYMON ŁȨSKI
Keyword(s):  
Initial Data ◽  
Wave Equations ◽  
Space Time ◽  
Einstein Equations ◽  
Nonlinear Wave Equations ◽  
Linear Wave ◽  
Cauchy Problems ◽  
Time Dimension ◽  
Wave Maps ◽  
Corner Conditions

The study of Einstein equations leads naturally to Cauchy problems with initial data on hypersurfaces which closely resemble hyperboloids in Minkowski space-time, and with initial data with polyhomogeneous asymptotics, that is, with asymptotic expansions in terms of powers of ln r and inverse powers of r. Such expansions also arise in the conformal method for analysing wave equations in odd space-time dimension. In recent work it has been shown that for non-linear wave equations, or for wave maps, polyhomogeneous initial data lead to solutions which are also polyhomogeneous provided that an infinite hierarchy of corner conditions holds. In this paper we show that the result is true regardless of corner conditions.

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