Related papers: Explicit form for the most general Lorentz transfo…
We show that by adding suitable lower-order terms to the Z4 formulation of the Einstein equations, all constraint violations except constant modes are damped. This makes the Z4 formulation a particularly simple example of a lambda-system as…
We first derive without recourse to the Dirac equation the two-component Majorana equation with a mass term by a direct linearization of the relativistic dispersion relation of a massive particle. Thereby, we make only use of the complex…
The partition function of the symmetric (zero electric field) eight-vertex model on a square lattice can be formulated either in the original "electric" vertex format or in an equivalent "magnetic" Ising-spin format. In this paper, both…
We present the first formulation of linearised gravity in four dimensions which is manifestly Lorentz covariant and democratic, i.e. treats the two frames related by electric-magnetic duality on equal footing. It is well-known that…
We present a novel representation of the Lorentz group, the geometric version of which uses "reversions" of a sphere while the algebraic version uses pseudounitary 2x2 matrices over complex numbers and quaternions, and Clifford algebras in…
This note presents explicit formulae for the exponentials of a wide variety of matrices which are 4x4, anti-Hermitian. Easily verifiable conditions characterizing when such matrices admit one of three minimal polynomials are also given.…
Simple unsmoothed formulas to compute the Riemann zeta function, and Dirichlet $L$-functions to a power-full modulus, are derived by elementary means (Taylor expansions and the geometric series). The formulas enable square-root of the…
For a relativistic charged particle moving in a constant electromagnetic field, its velocity 4-vector has been well studied. However, despite the fact that both the electromagnetic field and the equations of motion are purely real, the…
We probe the influence of Lorentz-violating mechanism, treated exactly, on the radiative quantum corrections to critical exponents for massive $q$-deformed O($N$) $\lambda\phi^{4}$ scalar field theories. We attain that task by employing…
The problem of minimizing a (nonconvex) quadratic form over the unit simplex, referred to as a standard quadratic program, admits an exact convex conic formulation over the computationally intractable cone of completely positive matrices.…
Commutative complex numbers of the form u=x+\alpha y+\beta z+\gamma t in 4 dimensions are studied, the variables x, y, z and t being real numbers. Four distinct types of multiplication rules for the complex bases \alpha, \beta and \gamma…
Several fundamental results in physics are derived from the simple starting point of two commuting orthogonal unit vectors. The combination of these unit vectors leads to spherical harmonics and Schwinger's expression of the…
We present an explicit formula for the expected value of a product of several independent symplectically invariant matrices in which the trace and real part function may be applied, possibly to different subexpressions. This takes the form…
When utilizing a cluster decomposible relativistic scattering formalism, it is most convenient that the covariant field equations take on a linear form with respect to the energy and momentum dispersion on the fields in the manner given by…
We present algebraic projective geometry definitions of 3D rotations so as to bridge a small gap between the applications and the definitions of 3D rotations in homogeneous matrix form. A general homogeneous matrix formulation to 3D…
A Lorentz non-invariant higher derivative effective action in flat spacetime, characterised by a constant vector, can be made invariant under infinitesimal Lorentz transformations by restricting the allowed field configurations. These…
Starting with the generators of the Poincar\'e group for arbitrary mass (m) and spin (s) a nonunitary transformation is implemented to obtain momenta with an absolute Planck scale limit. In the rest frame (for $m>0$) the transformed energy…
It has been suggested that one may construct a Lorentz-invariant noncommutative field theory by extending the coordinate algebra to additional, fictitious coordinates that transform nontrivially under the Lorentz group. Integration over…
The effect of different boost expressions, pertinent to the instant, front and point forms of relativistic quantum mechanics, is considered for the calculation of the ground-state form factor of a two-body system in simple scalar models.…
Using the notion, developed in an earlier paper, of "representation" of "position" by a vector in a vector space with an inner product, we show that the Lorentz Transformation Equations relating positions in two different reference frames…