scope of the present paper, and we just point out the possibility to extend our result to quantum spins here. In summary, the role of angular momentum in relativistic statistical mechanics has been
this inverse temperature bi-vector from the view point of statistical mechanics. We seek for the equilibrium distribution by maximizing the entropy under the constraints of conservation laws. The ... foundation of this approach may be highly conceptual and unsolved enigma in statistical mechanics. We may attribute its basis to the ergodic assumption of conventional statistical mechanics, or maximum entropy
In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum's theorem describes the relationship between the original and the associated Hamiltonian systems, which are iso-spectral ... energy state. Its counterpart in 'discrete' quantum mechanics is formulated algebraically, elucidating the basic structure of the discrete quantum mechanics, whose Schrodinger equation is a difference
In one-dimensional quantum mechanics, or the Sturm-Liouville theory, Crum's theorem describes the relationship between the original and the associated Hamiltonian systems, which are iso-spectral
Crum's theorem in one-dimensional quantum mechanics asserts the existence of an associated Hamiltonian system for any given Hamiltonian with the complete set of eigenvalues and eigenfunctions. The ... Crum's theorem for the 'discrete' quantum mechanics developed by two of the present authors. - §2. Ordinary quantum mechanics 2.1. Adler’s modification of Crum’s theorem 0 = E0 < E1 < E2 < · · · . H
Crum's theorem in one-dimensional quantum mechanics asserts the existence of an associated Hamiltonian system for any given Hamiltonian with the complete set of eigenvalues and eigenfunctions. The ... modification based on Crum's theorem for the 'discrete' quantum mechanics developed by two of the present authors. - energy levels are deleted. If the original system has polynomial eigenfunctions, as is
fluctuation theorem vanishes under the commutablecoupling condition. Conclusions will be presented in 5. 2. Exchange fluctuation theorem in quantum mechanics 2.1. Joint probability In this section, we define ... in quantum mechanics is described by an antilinear operator .24) The time-reversal invariance of the system is then expressed as The commutation relations in Eq. (2.11) are equivalent to the
exchange fluctuation theorem vanishes under the commutablecoupling condition. Conclusions will be presented in §5. §2. Exchange fluctuation theorem in quantum mechanics 2.1. Joint probability In this ... in quantum mechanics is described by an antilinear operator Θ.24) The time-reversal invariance of the system is then expressed as [Θ, HA] = 0, [Θ, Hc] = 0. [Θ, HB] = 0, [Θ, Πm] = 0. The commutation
In this article, we present a concise and self-contained introduction to nonequilibrium statistical mechanics with quantum field theory by considering an ensemble of interacting identical bosons or ... fermions as an example. Readers are assumed to be familiar with the Matsubara formalism of equilibrium statistical mechanics such as Feynman diagrams, the proper self-energy, and Dyson's equation. The aims
In this article, we present a concise and self-contained introduction to nonequilibrium statistical mechanics with quantum field theory by considering an ensemble of interacting identical bosons or ... fermions as an example. Readers are assumed to be familiar with the Matsubara formalism of equilibrium statistical mechanics such as Feynman diagrams, the proper self-energy, and Dyson's equation. The aims
Some examples in new quantum mechanics with the Riemannian energy-momentum space are described. ... our new quantum mechanics in the two cases (i) and (ii) described in 2.2 of I. All the formulae and results are, strictly speaking, correct in RF-CBR or FFLS (Rest Frame of Cosmic Background Radiation
) the covariant derivative Dj with respect to pj , This operator acts, e.g., when applied to a vector field Vρ as 1 i xj = Dj . Some examples in new quantum mechanics with the Riemannian energy-momentum ... mechanics (QM), where the momentum p of a particle is much smaller than its mass m (p << m), and usually m << K. The introduction of K into our QM is mostly of mathematical interest. However, if very massive
We propose a generalization of Heisenberg's matrix mechanics based on many-index objects. It is shown that there exists a solution describing a harmonic oscillator and that the many-index objects ... experimental results could be explained with classical mechanics (CM). The phenomenon of black body radiation destroyed this belief, and the concept of energy quanta was introduced by Planck in 1900 to overcome
We propose a generalization of Heisenberg's matrix mechanics based on many-index objects. It is shown that there exists a solution describing a harmonic oscillator and that the many-index objects ... . - objects lead to a generalization of spin algebra. A conjecture concerning operator formalism is also given. This paper is organized as follows. In the next section, we review Heisenberg’s matrix mechanics
A simple conformal quantum mechanics model of a d-component variable is proposed, which exactly reproduces the retarded Green functions and conformal weights of conformally coupled scalar fields in ... scalar fields with nonconformal coupling x = 12 . In this paper, a simple conformal quantum mechanics model of d-component variables, xi( ) (i = 1, .., d), is proposed, which exactly reproduces the
A simple conformal quantum mechanics model of a d-component variable is proposed, which exactly reproduces the retarded Green functions and conformal weights of conformally coupled scalar fields in ... . In this paper, a simple conformal quantum mechanics model of d-component variables, xi(? ) (i = 1, .., d), is proposed, which exactly reproduces the retarded Green functions and conformal weights of
We propose a new field-theoretic framework for formulating the non-relativistic quantum mechanics of D particles (D0 branes) in a Fock space of U(N) Yang-Mills theories with all different N ... , are defined. The base space of these D-particle fields is a (complex) vector space of infinite dimension. The gauge invariance of Yang-Mills quantum mechanics is reinterpreted as a quantum-statistical
field-theoretic framework for formulating the non-relativistic quantum mechanics of D particles (D0 branes) in a Fock space of U(N ) Yang-Mills theories with all different N simultaneously. D-particle ... . The gauge invariance of Yang-Mills quantum mechanics is reinterpreted as a quantum-statistical symmetry, which is taken into account by setting up a novel algebraic and projective structure in the
. Phys. , 1972 , vol. 27 https://doi.org/10.1007/BF01649654 17) Landau L. D. , Lifshitz E. M. . , Quantum Mechanics (Non-relativistic Theory) , 1977 3rd edition Oxford
We propose a large N vector quantum mechanics as the theory describing a D-particle probe in bubbling supertube solutions. We compute the effective action of this quantum mechanics and show that it ... quantum mechanics that describes the dynamics of these particles. Unfortunately, we have not succeeded in constructing such a quantum mechanics for an entire system of bound particles. In this paper, we