scholarly journals Infrared Problem vs Gauge Choice: Scattering of Classical Dirac Field

2021 ◽  
Author(s):  
Andrzej Herdegen
Keyword(s):  
Free Field ◽  
Asymptotic Completeness ◽  
Dirac Field ◽  
Free Evolution ◽  
Wave Operators ◽  
Radiation Fields ◽  
Scattering Wave ◽  
Long Time ◽  
Free Fields ◽  
External Time

AbstractWe consider the Dirac equation for the classical spinor field placed in an external, time-dependent electromagnetic field of the form typical for scattering settings: $$F=F^\mathrm{ret}+F^\mathrm{in}=F^\mathrm{adv}+F^\mathrm{out}$$ F = F ret + F in = F adv + F out , where the current producing $$F^{\mathrm{ret}/\mathrm{adv}}$$ F ret / adv has past and future asymptotes homogeneous of degree $$-3$$ - 3 , and the free fields $$F^{\mathrm{in}/\mathrm{out}}$$ F in / out are radiation fields produced by currents with similar asymptotic behavior. We show the existence of the electromagnetic gauges in which the particle has ‘in’ and ‘out’ asymptotic states approaching free field states, with no long-time corrections of the free dynamics. Using a special Cauchy foliation of the spacetime, we show in this context the existence and asymptotic completeness of the wave operators. Moreover, we define a special ‘evolution picture’ in which the free evolution operator has well-defined limits for $$t\rightarrow \pm \infty $$ t → ± ∞ ; thus the scattering wave operators do not need the free evolution counteraction.

scholarly journals Electromagnetic Gauge Choice for Scattering of Schrödinger Particle

2019 ◽  
Vol 20 (11) ◽  
pp. 3633-3650
Author(s):  
Andrzej Herdegen
Keyword(s):  
Asymptotic Behavior ◽  
External Electromagnetic Field ◽  
Asymptotic Completeness ◽  
Free Evolution ◽  
Wave Operators ◽  
Radiation Fields ◽  
Mechanical Evolution ◽  
Scattering Wave ◽  
Free Fields

Abstract We consider a Schrödinger particle placed in an external electromagnetic field of the form typical for scattering settings in the field theory: $$F=F^\mathrm {ret}+F^\mathrm {in}=F^\mathrm {adv}+F^\mathrm {out}$$ F = F ret + F in = F adv + F out , where the current producing $$F^{\mathrm {ret}/\mathrm {adv}}$$ F ret / adv has the past and future asymptotes homogeneous of degree $$-3$$ - 3 , and the free fields $$F^{\mathrm {in}/\mathrm {out}}$$ F in / out are radiation fields produced by currents with similar asymptotic behavior. We show that with appropriate choice of electromagnetic gauge the particle has ‘in’ and ‘out’ states reached with no further modification of the asymptotic dynamics. We use a special quantum mechanical evolution ‘picture’ in which the free evolution operator has well-defined limits for $$t\rightarrow \pm \infty $$ t → ± ∞ , and thus the scattering wave operators do not need the free evolution counteraction. The existence of wave operators in this setting is established, but the proof of asymptotic completeness is not complete: more precise characterization of the asymptotic behavior of the particle for $$|\mathbf {x}|=|t|$$ | x | = | t | would be needed.

2d QUANTUM DOTS IN POLYCHROMATIC RADIATION FIELDS: EFFECTS OF FREQUENCY MIXING, PHASE AND ANHARMONICITY ON THE FREEZING OF DYNAMICS

2010 ◽  
Vol 09 (01) ◽  
pp. 293-314
Author(s):  
SUBHASREE GHOSH ◽  
PARIKSHIT MANDAL ◽  
MANAS GHOSH
Keyword(s):  
Radiation Field ◽  
Time Dynamics ◽  
Radiation Fields ◽  
Single Carrier ◽  
Long Time ◽  
Oscillation Frequencies ◽  
Quartic Anharmonicity ◽  
External Time ◽  
Polychromatic Radiation ◽  
Insight Into

We explore the pattern of time evolution of a harmonically confined single carrier 2-d quantum dot when an external time varying polychromatic radiation field is switched on. The radiation field is composed of four mutually prime "nonresonant" frequencies. For given strengths of the confining field, cyclotron frequency, intensities, and oscillation frequencies of the external field, the system reveals a counter-intuitive long-time dynamics leading to a kind of localization in the unperturbed state space. The presence of cubic and quartic anharmonicity in the confining fields, and phase shifts in the external radiation fields, bring in new features in the dynamics. Time dependent Hellman–Feynmann theorem is invoked to gain insight into the frequency resolved absorption spectrum.

scholarly journals Generic nature of asymptotic completeness in dissipative scattering theory

2020 ◽  
pp. 2060001
Author(s):  
Jérémy Faupin
Keyword(s):  
Scattering Theory ◽  
Optical Model ◽  
Asymptotic Completeness ◽  
Quantum Systems ◽  
The Self ◽  
Wave Operators ◽  
Effective Dynamics ◽  
Long Time ◽  
Dissipative Quantum Systems ◽  
Pure States

We review recent results obtained in the scattering theory of dissipative quantum systems representing the long-time evolution of a system [Formula: see text] interacting with another system [Formula: see text] and susceptible of being absorbed by [Formula: see text]. The effective dynamics of [Formula: see text] is generated by an operator of the form [Formula: see text] on the Hilbert space of the pure states of [Formula: see text], where [Formula: see text] is the self-adjoint generator of the free dynamics of [Formula: see text], [Formula: see text] is symmetric and [Formula: see text] is bounded. The main example is a neutron interacting with a nucleus in the nuclear optical model. We recall the basic objects of the scattering theory for the pair [Formula: see text], as well as the results, proven in [10, 11], on the spectral singularities of [Formula: see text] and the asymptotic completeness of the wave operators. Next, for the nuclear optical model, we show that asymptotic completeness generically holds.

scholarly journals GENERALIZED W3-STRINGS FROM FREE FIELDS

1995 ◽  
Vol 10 (06) ◽  
pp. 515-524 ◽  
Author(s):  
J. M. FIGUEROA-O'FARRILL ◽  
C. M. HULL ◽  
L. PALACIOS ◽  
E. RAMOS
Keyword(s):  
Bosonic Strings ◽  
Free Field ◽  
Space Time ◽  
General Construction ◽  
Special Cases ◽  
Free Fields ◽  
Rule Out ◽  
General Conditions ◽  
String Theories

The conventional quantization of w3-strings gives theories which are equivalent to special cases of bosonic strings. We explore whether a more general quantization can lead to new generalized W3-string theories by seeking to construct quantum BRST charges directly without requiring the existence of a quantum W3-algebra. We study W3-like strings with a direct space-time interpretation — that is, with matter given by explicit free field realizations. Special emphasis is placed on the attempt to construct a quantum W-string associated with the magic realizations of the classical w3-algebra. We give the general conditions for the existence of W3-like strings, and comment on how the known results fit into our general construction. Our results are negative: we find no new consistent string theories, and in particular rule out the possibility of critical strings based on the magic realizations.

Free Quantum Fields

2020 ◽  
pp. 247-260
Author(s):  
Daniel Canarutto
Keyword(s):  
Free Field ◽  
Gauge Fields ◽  
Quantum Field ◽  
Quantum Fields ◽  
Dirac Fields ◽  
Free Fields ◽  
Explicit Expressions

The notion of free quantum field is thoroughly discussed in the linearised setting associated with the choice of a detector. The discussion requires attention to certain details that are often overlooked in the standard literature. Explicit expressions for generic fields, Dirac fields, gauge fields and ghost fields are laid down, as well the ensuing free-field expressions of important functionals. The relations between super-commutators of free fields and propagators, and the canonical super-commutation rules, follow from the above results.

Causal amplitudes and the Yang-Feldman formalism

1957 ◽  
Vol 53 (4) ◽  
pp. 843-847 ◽  
Author(s):  
J. C. Polkinghorne
Keyword(s):  
Field Theory ◽  
Green’S Functions ◽  
Free Field ◽  
Dispersion Relations ◽  
Matrix Elements ◽  
Field Equations ◽  
Commutation Relations ◽  
The Matrix ◽  
Free Fields ◽  
Set Up

ABSTRACTThe Yang-Feldman formalism vising the Feynman-like Green's functions is set up. The corresponding free fields have non-trivial commutation relations and contain information about the scattering. S-matrix elements are simply the matrix elements of anti-normal products of the field φF′(x). These are evaluated, and they give directly expressions used in the theory of causality and dispersion relations. It is possible to formulate field theory in a form in which the fields obey free field equations and the effects of interaction are contained in their commutation relations.

scholarly journals A NOTE ON KERR/CFT AND FREE FIELDS

2010 ◽  
Vol 25 (20) ◽  
pp. 3965-3973 ◽  
Author(s):  
JØRGEN RASMUSSEN
Keyword(s):  
Black Hole ◽  
Boundary Conditions ◽  
Isometry Group ◽  
Free Field ◽  
Kerr Black Hole ◽  
Virasoro Algebra ◽  
Free Fields ◽  
Horizon Geometry

The near-horizon geometry of the extremal four-dimensional Kerr black hole and certain generalizations thereof has an SL (2, ℝ) × U (1) isometry group. Excitations around this geometry can be controlled by imposing appropriate boundary conditions. For certain boundary conditions, the U(1) isometry is enhanced to a Virasoro algebra. Here, we propose a free-field construction of this Virasoro algebra.

scholarly journals WAVE PROPAGATION AND SCATTERING FOR THE RS2 BRANE COSMOLOGY MODEL

2009 ◽  
Vol 06 (04) ◽  
pp. 809-861 ◽  
Author(s):  
ALAIN BACHELOT
Keyword(s):  
Cauchy Problem ◽  
Scattering Theory ◽  
Scattering Matrix ◽  
Asymptotic Completeness ◽  
Decay Estimates ◽  
Brane Cosmology ◽  
Dispersive Waves ◽  
Wave Operators ◽  
Global Cauchy Problem

We study the wave equation for the gravitational fluctuations in the Randall–Sundrum brane cosmology model. We solve the global Cauchy problem and we establish that the solutions are the sum of a slowly decaying massless wave localized near the brane, and a superposition of massive dispersive waves. We compute the kernel of the truncated resolvent. We prove some L1-L∞, L2-L∞ decay estimates and global Lp Strichartz type inequalities. We develop the complete scattering theory: existence and asymptotic completeness of the wave operators, computation of the scattering matrix, determination of the resonances on the logarithmic Riemann surface.

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