Related papers: Quantum mechanics of higher derivative systems and…
Generalisations of the virial theorm in Classical Mechanics and Quantum Mechanics are examined. It is shown that the generalised virial theorem in Quantum Mechanics leads to certain relations between matrix elements. The differences between…
The phenomenon of universality is one of the most striking in many-body physics. Despite having sometimes wildly different microscopic constituents, systems can nonetheless behave in precisely the same way, with only the variable names…
We develop a new concept of quantum mechanics which is based on a generalized space-time and on an action vector space similar to it. Both spaces are provided by algebraic properties. This allows to calculate the Dirac matrixes and to…
A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…
Quantum mechanics is one of the basic theories of modern physics. Here, the famous Schr\"odinger equation and the differential operators representing mechanical quantities in quantum mechanics are derived, just based on the principle that…
In this article, we introduce higher derivative Lagrangians of this form $\alpha_1 A_{\mu}(x)\dot{x}^\mu$, $\alpha_2 G_{\mu}(x)\ddot{x}^\mu$, $\alpha_3 B_{\mu}(x)\dddot{x}^\mu$, $\alpha_4 K_{\mu}(x)\ddddot{x}^\mu$, $\cdots$, that generalize…
Quantum mechanics is usually presented starting from a series of postulates about the mathematical framework. In this work we show that those same postulates can be derived by assuming that measurements are discrete interactions: that is,…
Quantum mechanics is a special kind of description of motion. The concept of wave function itself implies the openness of quantum system. We show that quantum mechanics describes the quantum correlation, i.e., entanglement, and information…
Here I explore a novel no-collapse interpretation of quantum mechanics which combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical…
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantisation. We find that a 4-derivative degree of…
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…
The fundamental principle of quantum mechanics is that the probabilities of physical outcomes are obtained from the intermediate states and processes of the interacting particles, considered as happening concurrently. When the interaction…
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions…
A brief review of the physics of systems including higher derivatives in the Lagrangian is given. All such systems involve ghosts, i.e. the spectrum of the Hamiltonian is not bounded from below and the vacuum ground state is absent. Usually…
In the one-dimensional stationary case, we construct a mechanical Lagrangian describing the quantum motion of a non-relativistic spinless system. This Lagrangian is written as a difference between a function $T$, which represents the…
We present a complete theory, which is a generalization of Bargmann's theory of factors for ray representations. We apply the theory to the generally covariant formulation of the Quantum Mechanics.
Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in…
A formulation of quantum mechanics based on replacing the general unitary group by finite groups is considered. To solve problems arising in the context of this formulation, we use computer algebra and computational group theory methods.
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
On the basis of a manifestly covariant formalism of non-relativistic quantum mechanics in general coordinate systems, proposed by us recently, we derive general expressions for inertial forces. The results enable us further to discuss, and…