Conformal invariance and spontaneous symmetry breaking

Abstract

We study the spontaneous symmetry breaking in a conformally invariant gravitational theory. We particularly emphasize on the nonminimal coupling of matter fields to gravity. By the nonminimal coupling we consider a local distinction between the conformal frames of metric of matter fields and the metric explicitly entering the vacuum sector. We suppose that these two frames are conformally related by a dilaton field. We show that the imposition of a condition on the variable mass term of a scalar field may lead to the spontaneous symmetry breaking. In this way the scalar field may imitate the Higgs field behavior. Attributing a constant configuration to the ground state of the Higgs field, a Higgs conformal frame is specified. We define the Higgs conformal frame as a cosmological frame which describes the large scale characteristics of the observed universe. In the cosmological frame the gravitational coupling acquires a correct value and one no longer deals with the vacuum energy problem. We then study a more general case by considering a variable configuration for the ground state of Higgs field. In this case we introduce a cosmological solution of the model.

The bound state solution for the Morse potential with a localized mass profile

“…Then, by applying some simple constraints, on the terms included in the mass function, we construct the mass function in such a way that the corresponding equation can be solved via the Laplace transformation method used in Refs. [3] and [46]. The obtained mass distribution is a physical one, that is positivevalued, convergent, and well localized around the equilibrium position of a typical molecule.…”

“…The concept of the local mass has interesting features in the large scale characteristics of the universe and in gravitational field theories. [1][2][3][4] The position-dependent mass distribution also has received a great deal of attention in more terrestrial sciences, such as the material science, condensed matter physics, and semiconductors nanosubstructures, [5][6][7] quantum wells and quantum dots, [8][9][10] quantum liquids, [11] impurities in crystals, [12] and 3 He clusters. [13,14] The Hermitian Hamiltonian of von Roos with local mass distribution m = m(𝑟) is given by, [5]…”

Cosmological constant implementing Mach principle in general relativity

“…As in this regard, many interesting results have been obtained by applying this symmetry, see, e.g., Refs. [19]- [25].…”

“…6 However, in general, one can assume that the metrics in the gravitational and the matter parts are different (although conformally related), and achieves interesting results, see, e.g., Ref. [25]. and as usual the symmetric energy-momentum tensor of matter is defined as T µν ≡ − (2/ √ −g)× δS m /δg µν .…”

Solutions of Morse potential with position-dependent mass by Laplace transform

“…The concept of local mass has important consequences in the scalar tensor theories of gravity. This concept has interesting features in the gravitational quantum field theories [4]. The local mass concept also has been proliferated in more applicable sciences such as the material science and condensed matter physics.…”