scholarly journals Moyal Bracket and Ehrenfest’s Theorem in Born–Jordan Quantization

2019 ◽  
Vol 1 (1) ◽  
pp. 71-81
Author(s):  
Maurice de Gosson ◽  
Franz Luef
Keyword(s):  
Poisson Bracket ◽  
Time Evolution ◽  
Quantization Rule ◽  
Weyl Correspondence

The usual Poisson bracket { A , B } can be identified with the so-called Moyal bracket { A , B } M for larger classes of symbols than was previously thought, provided that one uses the Born–Jordan quantization rule instead of the better known Weyl correspondence. We apply our results to a generalized version of Ehrenfest’s theorem on the time evolution of averages of operators.

PRINCIPLES OF A NEW QUANTUM THEORY

1998 ◽  
Vol 13 (21) ◽  
pp. 1675-1688 ◽  
Author(s):  
C. SYROS
Keyword(s):  
Quantum Theory ◽  
Time Evolution ◽  
Evolution Operator ◽  
Quantization Rule ◽  
Time Evolution Operator ◽  
Standard Quantum ◽  
Time Space ◽  
Field Action ◽  
Time Quantum ◽  
Time’S Arrow

The principles of a random quantum theory (R-QT) which is alternatively time-asymmetric or time-symmetric if the quantization is Fermi–Dirac or Bose–Enstein, respectively are presented. Bohr's quantization rule is applied on the field-action integral. A time topological space, [Formula: see text], is mathematically defined in which the paradoxes in standard quantum theory are solved. The time "quantum", is created as a regular, positive into-map of an observed observable's change resulting from a fundamental interaction process. [Formula: see text] is constructed as the union of time elements and can be embedded disconnectedly in the continuous Newtonian universal time, [Formula: see text]. Six axioms are formulated characterizing the space–time and R-QT. The disconnectedness of the (κ×λκ)-fold time-space, [Formula: see text], imparts a kind of disconnectedness to the κ×λκ-fold space–times, [Formula: see text], and induces the chrono-topology. In chrono-topology the unitary, U, or non-measure preserving, R, dynamics, is implemented by means of a time evolution, "complex" operator, [Formula: see text]. It breaks down by means of Bohr quantization into: [Formula: see text][Formula: see text] coincides formally — apart from the spontaneous renormalization — with the time evolution operator in the standard QFT. [Formula: see text] is a novum and produces the Maxwell–Boltzmann energy level distribution in a non-Euclidean QFT. Compatibility between time-reversal invariance of the standard QT equations and irreversibility of some phenomena both in microcosmos and macrocosmos is obtained. The [Formula: see text]-evolution leads to a time's arrow on quantum-scale systems.

A COMPARISON BETWEEN ZIRCON-RUTILE THERMOMETRY OF ECLOGITES: IMPLICATIONS FOR TEMPERATURE-TIME EVOLUTION OF THE NORTH QAIDAM UHP TERRANE, CHINA

2017 ◽  
Author(s):  
David Hernández-Uribe ◽  
◽  
Chris G. Mattinson ◽  
Owen K. Neill ◽  
Andrew Kylander-Clark ◽  
...  
Keyword(s):  
Time Evolution ◽  
The North ◽  
North Qaidam ◽  
Temperature Time

Historical Background

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Steady State ◽  
Kinetic Theory ◽  
Time Evolution ◽  
Historical Development ◽  
Historical Background ◽  
Quantum Kinetic Theory ◽  
Dense Gases ◽  
Nonequilibrium Phenomena ◽  
Quantum Liquids ◽  
Nonlocal Quantum

The historical development of kinetic theory is reviewed with respect to the inclusion of virial corrections. Here the theory of dense gases differs from quantum liquids. While the first one leads to Enskog-type of corrections to the kinetic theory, the latter ones are described by quasiparticle concepts of Landau-type theories. A unifying kinetic theory is envisaged by the nonlocal quantum kinetic theory. Nonequilibrium phenomena are the essential processes which occur in nature. Any evolution is built up of involved causal networks which may render a new state of quality in the course of time evolution. The steady state or equilibrium is rather the exception in nature, if not a theoretical abstraction at all.

scholarly journals The time-dependent angular analysis of Bd → KSℓℓ, a new benchmark for new physics

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Sébastien Descotes-Genon ◽  
Martín Novoa-Brunet ◽  
K. Keri Vos
Keyword(s):  
Time Evolution ◽  
Form Factors ◽  
New Physics ◽  
Time Dependent ◽  
Angular Analysis ◽  
Time Dependent Analysis ◽  
Tensor Operators

Abstract We consider the time-dependent analysis of Bd→ KSℓℓ taking into account the time-evolution of the Bd meson and its mixing into $$ {\overline{B}}_d $$ B ¯ d . We discuss the angular conventions required to define the angular observables in a transparent way with respect to CP conjugation. The inclusion of time evolution allows us to identify six new observables, out of which three could be accessed from a time-dependent tagged analysis. We also show that these observables could be obtained by time-integrated measurements in a hadronic environment if flavour tagging is available. We provide simple and precise predictions for these observables in the SM and in NP models with real contributions to SM and chirally flipped operators, which are independent of form factors and charm-loop contributions. As such, these observables provide robust and powerful cross-checks of the New Physics scenarios currently favoured by global fits to b → sℓℓ data. In addition, we discuss the sensitivity of these observables with respect to NP scenarios involving scalar and tensor operators, or CP-violating phases. We illustrate how these new observables can provide a benchmark to discriminate among the various NP scenarios in b → sμμ. We discuss the extension of these results for Bs decays into f0, η or η′.

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