Related papers: Covariant and Contravariant Vectors
For generalized coordinate systems, the numerical values of vector and tensor components do not generally equal the physical values, i.e., the values one would measure with standard physical instruments. Hence, calculating physical…
We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies obtained for linear systems without zero order term in bounded domains and…
Coherent-state representations are a standard tool to deal with continuous-variable systems, as they allow one to efficiently visualize quantum states in phase space. Here, we work out an alternative basis consisting of monomials on the…
INTRODUCTION This papers deals with partial differential equations of second order, linear, with constant and not constant coefficients, in two variables, which admit real characteristics. I face the study of PDEs with the mentality of the…
By means of associated structural invariants, we efficiently construct four biplanes of order 9 - except the one with the smallest automorphism group, that is found by Janko and Trung. The notion of non-transversal vector is introduced…
The baryon structure is investigated in a covariant diquark-quark model. In this approach baryons emerge as relativistic bound states of a constituent quark and a $0^{+}$ or $1^{+}$ diquark. After solving the Bethe-Salpeter Equation for the…
Beginning with the Everett-DeWitt many-worlds interpretation of quantum mechanics, there have been a series of proposals for how the state vector of a quantum system might be split at any instant into orthogonal branches, each of which…
Two vertices $a$ and $b$ in a graph $X$ are cospectral if the vertex-deleted subgraphs $X\setminus a$ and $X\setminus b$ have the same characteristic polynomial. In this paper we investigate a strengthening of this relation on vertices,…
The developments of special relativity and quantum mechanics marked the beginning of the modern physics age. The former has taught us that while space and time are frame dependent notions, there is a quantity -- the space-time interval --…
This paper deals with the model companion of an endomorphism acting on a vector space, possibly with extra structure. Given a theory $T$ that $\varnothing$-defines an infinite $K$-vector space $\mathbb{V}$ in every model, we set $T_\theta…
It is well known that correlations predicted by quantum mechanics cannot be explained by any classical (local-realistic) theory. The relative strength of quantum and classical correlations is usually studied in the context of Bell…
We investigate geometrical properties and inequalities satisfied by the complex difference body, in the sense of studying which of the classical ones for the difference body have an analog in the complex framework. Among others we give an…
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A…
The first clue, in the theory of relativity, the 4-vector force acting on a particle is orthogonal to the 4-vector velocity of the particle, this orthogonality means that there is some difference between the orthogonality and the usual…
In the framework of teleparallel equivalent of general relativity, we study a gravity theory where a scalar field beyond its minimal coupling, is also coupled with the vector torsion through a non-minimal derivative coupling. After a…
Continuing the analysis undertaken in previous articles, we discuss some features of non-self-adjoint operators and sesquilinear forms which are defined starting from two biorthogonal families of vectors, like the so-called generalized…
We consider sets of quantum observables corresponding to eutactic stars. Eutactic stars are systems of vectors which are the lower dimensional ``shadow'' image, the orthogonal view, of higher dimensional orthonormal bases. Although these…
Transports preserving the angle between two contravariant vector fields but changing their lengths proportional to their own lengths are introduced as `conformal' transports and investigated over spaces with one affine connection and…
In the context of Covariant Quantum Mechanics for a spin particle, we classify the ``quantum vector fields'', i.e. the projectable Hermitian vector fields of a complex bundle of complex dimension 2 over spacetime. Indeed, we prove that the…
We study invariant operators in general tensor models. We show that representation theory provides an efficient framework to count and classify invariants in tensor models. In continuation and completion of our earlier work, we present two…