The relativistic finite-difference SUSY Quantum Mechanics (QM) is developed. We show that it is connected in a natural way with the q-deformed SUSY Quantum Mechanics. Simple examples are given.

On the basis of a 5-dimensional form of space-time transformations nonrelativistic quantum mechanics is reformulated in a manifestly covariant manner. The resulting covariance resembles that of the conventional relativistic quantum mechanics.

We revise the problem of the quantization of relativistic particle, presenting a modified consistent canonical scheme, which allows one not only to include arbitrary backgrounds in the consideration but to get in course of the quanti-zation a consistent relativistic quantum mechanics, which reproduces literally the behavior of the one-particle sector of the corresponding quantum field. At the s...

Quantum mechanics and relativistic causality together imply nonlocality: nonlo-cal correlations (that violate the CHSH inequality) and nonlocal equations of motion (the Aharonov-Bohm effect). Can we invert the logical order? We consider a conjecture that nonlocality and relativistic causality together imply quantum mechanics. We show that correlations preserving relativistic causality can viola...

We revise the problem of the quantization of relativistic particle models (spinless and spinning), presenting a modified consistent canonical scheme. One of the main point of the modification is related to a principally new realization of the Hilbert space. It allows one not only to include arbitrary backgrounds in the consideration but to get in course of the quantization a consistent relativi...

1 Quantum Field Theory ( QFT ) Why We Need It? 7 1.1 Two Flavors of QFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 QFT as a Special Application of Quantum Mechanics . . . . . . . . . . . . . 8 1.3 QFT as a Fundamentally New Physics Relativistic Multiparticle Quantum Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.1 QFT as conven...

We study the time evolution of decaying particles in renormalizable models of Relativistic Quantum Field Theory. Significant differences between the latter and Non Relativistic QuantumMechanics are found —in particular, the Zeno effect seems to be absent in such RQFT models. Conventional renormalization yields finite time behaviour in some cases but fails to produce finite survival probabilitie...

I maintain that quantum mechanics is fundamentally about a system of N particles evolving in three-dimensional space, not the wave function evolving in 3N-dimensional space. 1. Introduction. What is quantum mechanics fundamentally about? I believe that quantum mechanics is fundamentally about particles: quantum mechanics describes the behavior of systems of particles evolving in three-dimension...

Several recent arguments purport to show that there can be no relativistic, quantum-mechanical theory of localizable particles and, thus, that relativity and quantum mechanics can be reconciled only in the context of quantum field theory. We point out some loopholes in the existing arguments, and we provide two no-go theorems to close these loopholes. However, even with these loopholes closed, ...

Several recent arguments purport to show that there can be no relativistic, quantum-mechanical theory of localizable particles and, thus, that relativity and quantum mechanics can be reconciled only in the context of quantum field theory. We point out some loopholes in the existing arguments, and we provide two no-go theorems to close these loopholes. However, even with these loopholes closed, ...