Untitled

Abstract

Our primary task is to demonstrate that the logarithmic nonlinearity in the quantum wave equation can cause the spontaneous symmetry breaking and mass generation phenomena on its own, at least in principle. To achieve this goal, we view the physical vacuum as a kind of the fundamental Bose-Einstein condensate embedded into the fictitious Euclidean space. The relation of such description to that of the physical (relativistic) observer is established via the fluid/gravity correspondence map, the related issues, such as the induced gravity and scalar field, relativistic postulates, Mach's principle and cosmology, are discussed. For estimate the values of the generated masses of the otherwise massless particles such as the photon, we propose few simple models which take into account small vacuum fluctuations. It turns out that the photon's mass can be naturally expressed in terms of the elementary electrical charge and the extensive length parameter of the nonlinearity. Finally, we outline the topological properties of the logarithmic theory and corresponding solitonic solutions.

Canonical reduction for dilatonic gravity in3+1dimensions

“…Some versions of SVT favor a logarithmic Schrödinger equation [41]. Given the apparent resemblance between the Higgs boson and the dilaton mentioned earlier in the Introduction, the formulation herein could be fruitful in investigating this direction.…”

Classical and quantum cosmology with two perfect fluids: stiff matter and radiation

“…In addition, the theory allows us to establish the initial conditions for inflation, for primordial perturbations and for spontaneous symmetry breaking [5,6]. That is, the quantum cosmology is a theory of initial conditions.…”

Singularity-free model of electric charge in physical vacuum: non-zero spatial extent and mass generation

“…This has already been shown at the nonrelativistic level in [59], so in the current study we will investigate the relativistic case. The effective low-energy Lagrangian for the Maxwell field interacting with small fluctuations of the physical vacuum was proposed in [54], along with a mass generation mechanism which was analogous to the Higgs one. In this paper we propose a different mass generation mechanism which uses the same Lagrangian, except that the scalar potential is assumed to be "upended".…”

“…One of the candidate theories lies within the framework of the superfluid vacuum approach [46][47][48][49][50][51]. This theory is based on the idea [52][53][54] that a physical vacuum can be viewed as some sort of background superfluid condensate described by the logarithmic wave equation (the latter was studied previously on grounds of the dilatation covariance [55] or separability [56][57][58]). It was shown that small fluctuations of the logarithmic condensate obey the Lorentz symmetry and can be interpreted not only as the relativistic particle-like states but also as the gravitational ones [54] depending on a type of mode.…”

“…This theory is based on the idea [52][53][54] that a physical vacuum can be viewed as some sort of background superfluid condensate described by the logarithmic wave equation (the latter was studied previously on grounds of the dilatation covariance [55] or separability [56][57][58]). It was shown that small fluctuations of the logarithmic condensate obey the Lorentz symmetry and can be interpreted not only as the relativistic particle-like states but also as the gravitational ones [54] depending on a type of mode. In this approach, therefore, the Lorentz symmetry is not an exact symmetry of nature, but rather pertains to small fluctuations of the physical vacuum, and thus gets deformed at high energies and/or momenta.…”