Related papers: Some Lagrangians with Zeta Function Nonlocality
We establish a method to trace the Lagrangian evolution of extended objects consisting of a multicomponent scalar field in terms of a numerical calculation of field equations in three dimensional Eulerian meshes. We apply our method to the…
Massive integrable field theories in $1+1$ dimensions are defined at the Lagrangian level, whose classical equations of motion are related to the ``non-abelian'' Toda field equations. They can be thought of as generalizations of the…
Many attempts to introduce fundamental nonlocality into quantum (or classical) field theory are based on the assumption that exponentials of the d'Alembertian are positive-definite, so that these operators can be employed without…
In this paper, we introduce a new type of matter that has origin in $p$-adic strings, i.e., strings with a $p$-adic worldsheet. We investigate some properties of this $p$-adic matter, in particular its cosmological aspects. We start with…
We deform the standard four dimensional $\N=1$ superspace by making the odd coordinates $\theta$ not anticommuting, but satisfying a Clifford algebra. Consistency determines the other commutation relations of the coordinates. In particular,…
We prove a nonlocal, nonlinear commutator estimate concerning the transfer of derivatives onto testfunctions. For the fractional $p$-Laplace operator it implies that solutions to certain degenerate nonlocal equations are higher…
The classical Lagrange formalism is generalized to the case of arbitrary stationary (but not necessarily conservative) dynamical systems. It is shown that the equations of motion for such systems can be derived in the standard ways from the…
We introduce a new Tauberian framework through the theory of "regular arithmetic functions". This allows us to establish a characterization of the Riemann hypothesis by linking the floor function to the distribution of nontrivial zeros of…
A method for constructing general null Lagrangians and their higher harmonics is presented for dynamical systems with one degree of freedom. It is shown that these Lagrangians can be used to obtain non-standard Lagrangians, which give…
Treating inflation as an effective theory, we expect the effective Lagrangian to contain higher-dimensional kinetic operators suppressed by the scale of UV physics. When these operators are powers of the inflaton kinetic energy, the scalar…
The new manifestation of conformal invariance for a massless scalar particle in a Riemannian spacetime of general relativity is found. Conformal transformations conserve the Hamiltonian and wave function in the Foldy-Wouthuysen…
The chiral and scale anomalies of a very general class of non local Dirac operators are computed using the $\zeta$-function definition of the fermionic determinant. For the axial anomaly all new terms introduced by the non locality are…
A description of how the principle of stationary action reproduces itself in terms of the intrinsic geometry of variational equations is proposed. A notion of stationary points of an internal Lagrangian is introduced. A connection between…
This study of gauge field theories on kappa-deformed Minkowski spacetime extends previous work on field theories on this example of a noncommutative spacetime. We construct deformed gauge theories for arbitrary compact Lie groups using the…
We obtain formulas for the spectral zeta function of the Laplacian on symmetric finitely ramified fractals, such as the Sierpinski gasket, and a fractal Laplacian on the interval. These formulas contain a new type of zeta function…
Nonrelativstic effective field theories have shown to be a useful framework to describe systems of weakly bound particles. This work focuses on the matching procedure to the underlying relativistic theory. The concept of a physical mass in…
We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar…
The construction of effective Lagrangians commonly involves the application of the `classical equation of motion' to eliminate redundant structures and thus generate the minimal number of independent terms. We investigate this procedure in…
In 2017, this author proposed, as a resolution of the Measurement Problem, that terms be added to Schrodinger's wavefunction equation, rendering it nonlinear. Said equation derived from a trick employed by S. Weinberg in 1989 which may be…
We discuss construction of classical time dependent solutions in open string (field) theory, describing the motion of the tachyon on unstable D-branes. Despite the fact that the string field theory action contains infinite number of time…