Related papers: Time Operator in Relativistic Quantum Mechanics
Several quantum proper time derivatives are obtained from the Beck one in the usual framework of relativistic quantum mechanics (spin 1/2 case). The ``scalar Hamiltonians'' of these derivatives should be thought of as the conjugate…
We investigate time operators in the context of quantum time crystals in ring systems. A generalized commutation relation called the generalized weak Weyl relation is used to derive a class of self-adjoint time operators for ring systems…
The usual quantum mechanics describes the mass eigenstates. To describe the proper-time eigenstates, a duality theory of the usual quantum mechanics was developed. The time interval is treated as an operator on an equal footing with the…
A suitable operator for the time-of-arrival at a detector is defined for the free relativistic particle in 3+1 dimensions. For each detector position, there exists a subspace of detected states in the Hilbert space of solutions to the Klein…
We find all spin operators for a Dirac particle satisfying the following very general conditions: (i) spin does not convert positive (negative) energy states into negative (positive) energy states, (ii) spin is a pseudo-vector, and (iii)…
We have previously shown (arXiv:1912.00033) that three approaches to relational quantum dynamics -- relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations -- are equivalent. Here we show that this `trinity'…
The nonrelativistic Schroedinger equation for motion of a structureless particle in four-dimensional space-time entails a well-known expression for the conserved four-vector field of local probability density and current that are associated…
Similarly as classical propositional calculus is based algebraically on Boolean algebras, the logic of quantum mechanics was based on orthomodular lattices by G. Birkhoff and J. von Neumann and K. Husimi. However, this logic does not…
The problem of time in the quantization of gravity arises from the fact that time in Schroedinger's equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus "time"…
Quantum mechanical operators and quantum fields are interpreted as realizations of timespace manifolds. Such causal manifolds are parametrized by the classes of the positive unitary operations in all complex operations, i.e. by the…
The operational approach to time is a cornerstone of relativistic theories, as evidenced by the notion of proper time. In standard quantum mechanics, however, time is an external parameter. Recently, many attempts have been made to extend…
The existence of a classical limit describing interacting particles in a second-quantized theory of identical particles with bosonic symmetry is proved. This limit exists in addition to a previously established classical limit with a…
Frauchiger and Renner recently cast doubt on the universal applicability of Quantum Mechanics [1]. In the following, it is pointed out that their conclusion of one of three common-sense conditions, demanded for Quantum Mechanics, being…
We treat space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order Hamiltonian and momentum…
The positivity of the energy in relativistic quantum mechanics implies that wave functions can be continued analytically to the forward tube T in complex spacetime. For Klein-Gordon particles, we interpret T as an extended (8D) classical…
We present a derivation of a position operator for a massive field with spin $1/2$, expressed in a representation-independent form of the Poincar\'e group. Using the recently derived Lorentz-covariant field spin operator, we obtain a…
Seeking for a relativistic generalisation of the non-relativistic Schroedinger equation, one very soon arrives at equations with a square-root operator by having applied the quantum mechanical correspondence principle to the formula of…
In quantum mechanics time usually appears as classical parameter which means that it is treated as being essentially different from spatial coordinates that are represented by operators. On the other hand, relativity theory demands to treat…
We propose a manifestly Lorentz covariant, non-commutative Dirac equation for charged particles interacting with an electromagnetic field. The equation is formulated on the operator level, but operators are not composed through the normal…
We show that the first order form of the Schrodinger equation proposed in [1] can be obtained from the Dirac equation in the non-relativistic limit. We also show that the Pauli Hamiltonian is obtained from this equation by requiring local…