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"Minkowski space"
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Relativity without spacetime
\"In 1908, three years after Einstein first published his special theory of relativity, the mathematician Hermann Minkowski introduced his four-dimensional 'spacetime' interpretation of the theory. Einstein initially dismissed Minkowski's theory, remarking that 'since the mathematicians have invaded the theory of relativity I do not understand it myself anymore.' Yet Minkowski's theory soon found wide acceptance among physicists, including eventually Einstein himself, whose conversion to Minkowski's way of thinking was engendered by the realization that he could profitably employ it for the formulation of his new theory of gravity. The validity of Minkowski's mathematical 'merging' of space and time has rarely been questioned by either physicists or philosophers since Einstein incorporated it into his theory of gravity. Physicists often employ Minkowski spacetime with little regard to the whether it provides a true account of the physical world as opposed to a useful mathematical tool in the theory of relativity. Philosophers sometimes treat the philosophy of space and time as if it were a mere appendix to Minkowski's theory. Joseph Cosgrove subjects the concept of spacetime to a comprehensive examination and concludes that Einstein's initial assessment of Minkowksi was essentially correct\"--Back cover.
Book
The Global Nonlinear Stability of Minkowski Space for the Massless Einstein–Vlasov System
Minkowski space is shown to be globally stable as a solution to the Einstein–Vlasov system in the case when all particles have zero mass. The proof proceeds by showing that the matter must be supported in the “wave zone”, and then proving a small data semi-global existence result for the characteristic initial value problem for the massless Einstein–Vlasov system in this region. This relies on weighted estimates for the solution which, for the Vlasov part, are obtained by introducing the Sasaki metric on the mass shell and estimating Jacobi fields with respect to this metric by geometric quantities on the spacetime. The stability of Minkowski space result for the vacuum Einstein equations is then appealed to for the remaining regions.
Journal Article
Covariant Cubic Interacting Vertices for Massless and Massive Integer Higher Spin Fields
We develop the BRST approach to construct the general off-shell local Lorentz covariant cubic interaction vertices for irreducible massless and massive higher spin fields on d-dimensional Minkowski space. We consider two different cases for interacting higher spin fields: with one massive and two massless; two massive, both with coinciding and with different masses and one massless field of spins s1,s2,s3. Unlike the previous results on cubic vertices we extend our earlier result in (Buchbinder, I.L.; et al. Phys. Lett. B 2021, 820, 136470) for massless fields and employ the complete BRST operator, including the trace constraints, which is used to formulate an irreducible representation with definite integer spin. We generalize the cubic vertices proposed for reducible higher spin fields in (Metsaev, R.R. Phys. Lett. B 2013, 720, 237) in the form of multiplicative and non-multiplicative BRST-closed constituents and calculate the new contributions to the vertex, which contains the additional terms with a smaller number of space-time derivatives. We prove that without traceless conditions for the cubic vertices in (Metsaev, R.R. Phys. Lett. B 2013, 720, 237) it is impossible to provide the noncontradictory Lagrangian dynamics and find explicit traceless solution for these vertices. As the examples, we explicitly construct the interacting Lagrangians for the massive spin of the s field and the massless scalars, both with and without auxiliary fields. The interacting models with different combinations of triples higher spin fields: massive spin s with massless scalar and vector fields and with two vector fields; massless helicity λ with massless scalar and massive vector fields; two massive fields of spins s, 0 and massless scalar is also considered.
Journal Article
Generalized Bertrand Curves of Non-Light-like Framed Curves in Lorentz–Minkowski 3-Space
In this paper, we define the generalized Bertrand curves of non-light-like framed curves in Lorentz–Minkowski 3-space; their study is essential for understanding many classical and modern physics problems. Here, we consider two non-light-like framed curves as generalized Bertrand pairs. Our generalized Bertrand pairs can include Bertrand pairs with either singularities or not, and also include Mannheim pairs with singularities. In addition, we discuss their properties and prove the necessary and sufficient conditions for two non-light-like framed curves to be generalized Bertrand pairs.
Journal Article
Classification of Ruled Surfaces as Homothetic Self-Similar Solutions of the Inverse Mean Curvature Flow in the Lorentz–Minkowski 3-Space
In this paper, we classify the nondegenerate ruled surfaces in the three-dimensional Lorentz–Minkowski space that are homothetic self-similar solutions for the inverse mean curvature flow. This classification shows the existence of two classes of non-cylindrical homothetic solitons: one with lightlike rulings and another one with non-lightlike rulings.
Journal Article
Space-like maximal surfaces containing entire null lines in Lorentz-Minkowski 3-space
Consider a surface S immersed in the Lorentz-Minkowski 3-space [R.sup.3.sub.1]. A complete light-like line in [R.sup.3.sub.1] is called an entire null line on the surface S in [R.sup.3.sub.1] if it lies on S and consists of only null points with respect to the induced metric. In this paper, we show the existence of embedded space-like maximal graphs containing entire null lines. If such a graph is defined on a convex domain in [R.sup.2], then it must be contained in a light-like plane (cf. Remark 3.3). Our example is critical in the sense that it is defined on a certain non-convex domain. Key words: Maximal surface; type change; zero mean curvature; Lorentz-Minkowski space.
Journal Article
Lorentz quantum mechanics
We present a theoretical framework for the dynamics of bosonic Bogoliubov quasiparticles. We call it Lorentz quantum mechanics because the dynamics is a continuous complex Lorentz transformation in complex Minkowski space. In contrast, in usual quantum mechanics, the dynamics is the unitary transformation in Hilbert space. In our Lorentz quantum mechanics, three types of state exist: space-like, light-like and time-like. Fundamental aspects are explored in parallel to the usual quantum mechanics, such as a matrix form of a Lorentz transformation, and the construction of Pauli-like matrices for spinors. We also investigate the adiabatic evolution in these mechanics, as well as the associated Berry curvature and Chern number. Three typical physical systems, where bosonic Bogoliubov quasi-particles and their Lorentz quantum dynamics can arise, are presented. They are a one-dimensional fermion gas, Bose-Einstein condensate (or superfluid), and one-dimensional antiferromagnet.
Journal Article
Curves in Lightlike Planes in Three-Dimensional Lorentz–Minkowski Space
In this paper, we analyze the intrinsic geometry of lightlike planes in the three-dimensional Lorentz–Minkowski space M3. We connect the theory of curves lying in lightlike planes in M3 with the theory of curves in the simply isotropic plane I2. Based on these relations, we characterize some special classes of curves that lie in lightlike planes in M3.
Journal Article
Rarefied relativistic polyatomic gases in a gravitational field
The principal goal of the present paper is to study rarefied relativistic polyatomic gases in both Minkowski spacetime and Robertson–Walker spacetime. The field equations are determined from a recently developed generalized relativistic BGK-type model for polyatomic gases. This model is applied to both Minkowski spacetime and flat and non- flat Robertson–Walker spacetimes. The equation of state for the non-equilibrium dynamical pressure is obtained from the Chapman–Enskog method applied to a variant of the Anderson and Witting model for polyatomic gases.
Journal Article
Quantum Time
A short introduction, with extended interpretations, to the Projection Evolution approach is presented. In this model time is like the other space positions represented by an operator in the state space of a physical system. As a pedagogigal example the Minkowski spacetime is considered. Finally, a short analysis of the time reversal symmetry is presented.
Journal Article