scholarly journals Reparameterization invariant operator basis for NRQED and HQET

2019 ◽  
Vol 2019 (11) ◽  
Author(s):  
Andrew Kobach ◽  
Sridip Pal
Keyword(s):  
Invariant Operator

The pseudo Hermitian invariant operator and time-dependent non-Hermitian Hamiltonian exhibiting a SU(1,1) and SU(2) dynamical symmetry

2018 ◽  
Vol 59 (7) ◽  
pp. 072103 ◽  
Author(s):  
Walid Koussa ◽  
Naima Mana ◽  
Oum Kaltoum Djeghiour ◽  
Mustapha Maamache
Keyword(s):  
Dynamical Symmetry ◽  
Invariant Operator ◽  
Time Dependent

GEOMETRIC PHASES, SQUEEZED QUANTUM STATES AND GAUSSIAN WAVE PACKET STATES OF RELIC GRAVITONS

2012 ◽  
Vol 18 ◽  
pp. 13-17
Author(s):  
K. BAKKE ◽  
I. A. PEDROSA ◽  
C. FURTADO
Keyword(s):  
Wave Packet ◽  
Linear Time ◽  
Invariant Operator ◽  
Quantum States ◽  
Time Dependent ◽  
Gaussian Wave Packet ◽  
Geometric Phases ◽  
Uncertainty Product ◽  
Quantized Field ◽  
Generalized Time

In this contribution, we discuss quantum effects on relic gravitons described by the Friedmann-Robertson-Walker (FRW) spacetime background by reducing the problem to that of a generalized time-dependent harmonic oscillator, and find the corresponding Schrödinger states with the help of the dynamical invariant method. Then, by considering a quadratic time-dependent invariant operator, we show that we can obtain the geometric phases and squeezed quantum states for this system. Furthermore, we also show that we can construct Gaussian wave packet states by considering a linear time-dependent invariant operator. In both cases, we also discuss the uncertainty product for each mode of the quantized field.

Unitarily Invariant Operator Norms

1983 ◽  
Vol 35 (2) ◽  
pp. 274-299 ◽  
Author(s):  
C.-K. Fong ◽  
J. A. R. Holbrook
Keyword(s):  
Hilbert Space ◽  
Convex Functions ◽  
Invariant Operator ◽  
Space Operator ◽  
Numerical Radius ◽  
The Past ◽  
Operator Norms ◽  
Power Inequality ◽  
The Many ◽  
Image Position

1.1. Over the past 15 years there has grown up quite an extensive theory of operator norms related to the numerical radius1of a Hilbert space operator T. Among the many interesting developments, we may mention:(a) C. Berger's proof of the “power inequality”2(b) R. Bouldin's result that3for any isometry V commuting with T;(c) the unification by B. Sz.-Nagy and C. Foias, in their theory of ρ-dilations, of the Berger dilation for T with w(T) ≤ 1 and the earlier theory of strong unitary dilations (Nagy-dilations) for norm contractions;(d) the result by T. Ando and K. Nishio that the operator radii wρ(T) corresponding to the ρ-dilations of (c) are log-convex functions of ρ.

scholarly journals Quantization of a 3D Nonstationary Harmonic plus an Inverse Harmonic Potential System

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Salim Medjber ◽  
Hacene Bekkar ◽  
Salah Menouar ◽  
Jeong Ryeol Choi
Keyword(s):  
Separation Of Variables ◽  
Type Equation ◽  
Invariant Operator ◽  
Wave Functions ◽  
Time Dependent ◽  
Harmonic Potential ◽  
Uncertainty Relations ◽  
Mathematical Methods ◽  
Potential System ◽  
Uvarov Method

The Schrödinger solutions for a three-dimensional central potential system whose Hamiltonian is composed of a time-dependent harmonic plus an inverse harmonic potential are investigated. Because of the time-dependence of parameters, we cannot solve the Schrödinger solutions relying only on the conventional method of separation of variables. To overcome this difficulty, special mathematical methods, which are the invariant operator method, the unitary transformation method, and the Nikiforov-Uvarov method, are used when we derive solutions of the Schrödinger equation for the system. In particular, the Nikiforov-Uvarov method with an appropriate coordinate transformation enabled us to reduce the eigenvalue equation of the invariant operator, which is a second-order differential equation, to a hypergeometric-type equation that is convenient to treat. Through this procedure, we derived exact Schrödinger solutions (wave functions) of the system. It is confirmed that the wave functions are represented in terms of time-dependent radial functions, spherical harmonics, and general time-varying global phases. Such wave functions are useful for studying various quantum properties of the system. As an example, the uncertainty relations for position and momentum are derived by taking advantage of the wave functions.

UNITARY TRANSFORMATION APPROACH FOR THE PHASE OF THE DAMPED DRIVEN HARMONIC OSCILLATOR

2003 ◽  
Vol 17 (26) ◽  
pp. 1365-1376 ◽  
Author(s):  
JEONG-RYEOL CHOI
Keyword(s):  
Wave Function ◽  
Harmonic Oscillator ◽  
Unitary Transformation ◽  
Operator Method ◽  
Classical Equation ◽  
Transformation Method ◽  
Invariant Operator ◽  
Harmonic Oscillators ◽  
Parabolic Cylinder ◽  
Parabolic Cylinder Function

Using the invariant operator method and the unitary transformation method together, we obtained discrete and continuous solutions of the quantum damped driven harmonic oscillator. The wave function of the underdamped harmonic oscillator is expressed in terms of the Hermite polynomial while that of the overdamped harmonic oscillator is expressed in terms of the parabolic cylinder function. The eigenvalues of the underdamped harmonic oscillator are discrete while that of the critically damped and the overdamped harmonic oscillators are continuous. We derived the exact phases of the wave function for the underdamped, critically damped and overdamped driven harmonic oscillator. They are described in terms of the particular solutions of the classical equation of motion.

scholarly journals A COMPLETE AND MINIMAL CATALOGUE OF MSSM GAUGE INVARIANT MONOMIALS

2010 ◽  
Vol 25 (17) ◽  
pp. 3375-3387 ◽  
Author(s):  
ANDERS BASBØLL
Keyword(s):  
Linear Combination ◽  
Nonnegative Integer ◽  
Invariant Operator ◽  
Sixth Order ◽  
Gauge Invariant

We present a complete and minimal catalogue of MSSM gauge invariant monomials. That is, the catalogue of Gherghetta, Kolda and Martin is elaborated to include generational structure for all monomials. Any gauge invariant operator can be built as a linear combination of elements of the catalogue lifted to nonnegative integer powers. And the removal of any one of the monomials would deprive the catalogue of this feature. It contains 712 monomials, plus 3 generations of right-handed neutrinos if one extends the model to the νMSSM. We note that νMSSM flat directions can all be lifted by the sixth-order superpotential compared to the ninth-order needed in MSSM.

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