On the classical and quantum irrotational motions of a relativistic perfect fluid I. Classical theory

1985 ◽  
Vol 401 (1820) ◽  
pp. 53-66 ◽  
Keyword(s):  
Perfect Fluid ◽  
Vacuum State ◽  
Background Field ◽  
Field Configuration ◽  
Spontaneous Breaking ◽  
Sound Waves ◽  
Action Functional ◽  
Fluid Equation ◽  
Goldstone Bosons ◽  
General Relativistic

Some aspects of perfect-fluid general-relativistic hydrodynamics under the assumptions of irrotationality and isentropicity are analysed. A new derivation of the known fact that the Lagrangian for these fluids is just the pressure is given. Then we study the fluctuations around a given background field configuration, extracting a rule that connects the order at which a Taylor expansion of the action functional possibly stops with the fluid equation of state. From a classical invariance of the action we deduce the conserved Noether current. Because of the spontaneous breaking of such an invariance on the vacuum state Goldstone bosons arise, which turn out to be just phonons (quantized sound waves). Some useful results concerning the linear theory of sound waves are also given.

The Non-Metric Solution to Graviton as Goldstone Boson

2020 ◽  
Author(s):  
Aayush Verma
Keyword(s):  
Field Theory ◽  
Goldstone Boson ◽  
Vacuum State ◽  
Metric Tensor ◽  
Goldstone Bosons ◽  
Recent Advancement ◽  
Quantized Field ◽  
The 1960S ◽  
Extended Theories ◽  
Theories Of Gravitation

The study of Graviton as Goldstone bosons appeared in the 1960s, after Bjorken interacting idea of Electrodynamics. However, no recent advancement has been done in the field, because of very constraints as well as low-attractiveness of the theory. We do the non-metric tensor (covariant derivative of the metric tensor) case of Gravitation and eventually get SO(1,3) broken in the vacuum state of quantized field theory, then find the Graviton as Goldstone Boson. We, in final, see that Gravitons can have appearances in many modified (and extended) theories of Gravitation.

MAGNETIC FIELDS AND VACUUM POLARIZATION AT THE PLANCK ERA

2003 ◽  
Vol 12 (07) ◽  
pp. 1289-1298 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Vacuum State ◽  
Background Field ◽  
Unified Theory ◽  
Grand Unified Theory ◽  
Maxwell Theory ◽  
Yang Mills ◽  
Electron Positron ◽  
The One

The one-loop effective action describing polarization of the vacuum due to virtual electron-positron pairs in the Maxwell theory of electromagnetism was obtained by Heisenberg and Euler, in the limit of a background field that is constant on the scale of the electron Compton-wavelength. The case of vanishing electric field and constant, ultra-strong magnetic field B≫Bc, where [Formula: see text], yields a configuration whose energy density is less than that of the equivalent radiation field, suggesting why a magnetic field may be present in the early Universe back to the Planck era. For there is a similar but larger effect, allowing a "ferromagnetic" Yang–Mills vacuum state, in the grand-unified theory at temperatures [Formula: see text], analyzed by Skalozub. Some further aspects of ultra-strong magnetic fields are discussed vis-à-vis the origin of the Galactic field B g .

scholarly journals Classical simulation of quantum fields I

2006 ◽  
Vol 84 (10) ◽  
pp. 861-877 ◽  
Author(s):  
T Hirayama ◽  
B Holdom
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Zero Point ◽  
Background Field ◽  
Field Configuration ◽  
Classical Electrodynamics ◽  
Quantum Field ◽  
Point Energy ◽  
Classical Simulation ◽  
Feynman Rules

We study classical field theories in a background field configuration where all modes of the theory are excited, matching the zero-point energy spectrum of quantum field theory. Our construction involves elements of a theory of classical electrodynamics by Wheeler–Feynman and the theory of stochastic electrodynamics of Boyer. The nonperturbative effects of interactions in these theories can be very efficiently studied on the lattice. In [Formula: see text] theory in 1 + 1 dimensions, we find results, in particular, for mass renormalization and the critical coupling for symmetry breaking that are in agreement with their quantum counterparts. We then study the perturbative expansion of the n-point Green's functions and find a loop expansion very similar to that of quantum field theory. When compared to the usual Feynman rules, we find some differences associated with particular combinations of internal lines going on-shell simultaneously. PACS Nos.: 03.70.+k, 03.50.–z, 11.15.Tk

A NONSINGULAR PERFECT FLUID CLASSICAL LEPTON MODEL OF ARBITRARILY SMALL RADIUS

2013 ◽  
Vol 22 (14) ◽  
pp. 1350088 ◽  
Author(s):  
THOMAS E. KIESS
Keyword(s):  
Electric Field ◽  
Perfect Fluid ◽  
Small Radius ◽  
Spherically Symmetric ◽  
Model Based ◽  
Perfect Fluids ◽  
General Relativistic ◽  
Relativistic Models ◽  
Lepton Model

We exhibit a classical lepton model based on a perfect fluid that reproduces leptonic charges and masses in arbitrarily small volumes without metric singularities or pressure discontinuities. This solution is the first of this kind to our knowledge, because to date the only classical general relativistic models that have reproduced leptonic charges and masses in arbitrarily small volumes are based on imperfect (anisotopic) fluids or perfect fluids with electric field discontinuities. We use a Maxwell–Einstein exact metric for a spherically symmetric static perfect fluid in a region in which the pressure vanishes at a boundary, beyond which the metric is of the Reissner–Nordström form. This construction models lepton mass and charge in the limit as the boundary → 0.

scholarly journals Fluid dynamics in the Ellis wormhole

2021 ◽  
pp. 2150072
Author(s):  
G. Butbaia ◽  
Z. N. Osmanov
Keyword(s):  
Fluid Dynamics ◽  
Physical System ◽  
Continuity Equation ◽  
Radial Flow ◽  
Momentum Equation ◽  
Flow Dynamics ◽  
Sound Waves ◽  
General Relativistic

In the Ellis wormhole metrics, we study the characteristics of fluid dynamics and the properties of linear sound waves. By implying the energy–momentum equation and the continuity equation in the general relativistic manner, we examine the flow dynamics and solve the corresponding equations for a relatively simple case — radial flow. To study the linear sound waves, the equations governing the mentioned physical system are linearized and solved and interesting characteristic properties are found.

scholarly journals Ambartsumian’s vision and further insight to key puzzles of ultra-high energy astrophysics

2021 ◽  
pp. 236-310
Author(s):  
G. Ter-Kazarian
Keyword(s):  
Microscopic Theory ◽  
Vacuum State ◽  
High Energy ◽  
Spontaneous Breaking ◽  
Ultra High Energy ◽  
High Energy Astrophysics ◽  
Superdense Matter ◽  
Equilibrium Configurations ◽  
Accretion Physics ◽  
Stellar Masses

We review the Ambartsumian’s cosmogony, which involves his fundamental ideas on Stellar Associations and eruptive Activity of Galactic Nuclei, where the creation process is at work. Itis caused by the violent outburst events of transformations of superdense matter in supermassive compact bodies in galaxies, away from the accretion physics. We discuss the pioneering works of V.A. Armbartsumyan and G.S. Saakyan carried out at Byurakan Observatory in the earlier of 1960’s towards the physics of equilibrium configurations of degenerate superdense gas of elementary particles, particularity, the hyperon configurations of stellar masses. These issues have been comprehensively developed later on by G. Ter-Kazarian in the proposed theory of distortion of space-time continuum(DSTC) at huge energies (respectively, at short distances < 0.4fm), which underlies the microscopic theory of black hole (MTBH). The MTBH has further proved to be quite fruitful for ultra-high energy astrophysics. The MTBH explores the most important process of spontaneous breaking of gravitation gauge symmetry at huge energies, and thereof for that of re-arrangement of vacuum state. As a corollary, MTBH has smeared out the central singularities of BHs, and makes room for their growth and merging behavior, with implications of vital interest for high energy astrophysics.

scholarly journals Shear-free conditions of a Chaplygin-gas-dominated universe

2021 ◽  
pp. 2150192
Author(s):  
Amare Abebe ◽  
Mudhahir Al Ajmi ◽  
Maye Elmardi ◽  
Hemwati Nandan ◽  
Noor ul Sabah
Keyword(s):  
General Relativity ◽  
Perfect Fluid ◽  
Chaplygin Gas ◽  
Current Investigation ◽  
Free Condition ◽  
General Relativistic ◽  
Relativistic Framework ◽  
Fluid Spacetimes

In this work, we revisit the shear-free conjecture of general relativity and study the well-known shear-free condition in the context of the Chaplygin-gas cosmology. It had been shown in previous investigations that, in the general relativistic framework, the matter congruences of shear-free perfect fluid spacetimes should be either expansion-free or rotation-free. Our current investigation, however, indicates that a universe dominated by a Chaplygin-gas can allow a simultaneous expansion and rotation of the fluid provided that certain non-trivial conditions, which we derive and describe in what follows, are met. We also show that, in the appropriate limiting cases, our results reduce to the expected results of dust spacetimes which can only expand or rotate, but not both, at the same time.

Spontaneous breaking of Elliott symmetry in nuclear systems and thesanddNambu-Goldstone bosons

1991 ◽  
Vol 43 (6) ◽  
pp. 2891-2894 ◽  
Author(s):  
X. Q. Zhu ◽  
F. C. Khanna ◽  
H. Umezawa
Keyword(s):  
Spontaneous Breaking ◽  
Goldstone Bosons ◽  
Nuclear Systems

Standard covariant formulation for perfect-fluid dynamics

1988 ◽  
Vol 186 ◽  
pp. 1-24 ◽  
Author(s):  
B. Carter ◽  
B. Gaffet
Keyword(s):  
Perfect Fluid ◽  
Chemical Constituents ◽  
Standard Form ◽  
Space Time ◽  
Variation Principle ◽  
Covariant Formulation ◽  
Invariance Group ◽  
Dynamical Equations ◽  
General Relativistic ◽  
Derivatives Of

After a brief description of the Milne generalization of the Galilean invariance group for the space–time of Newtonian kinematics, it is shown how the generalized Eulerian dynamical equations for the motion of a multiconstituent perfect (nonconducting) fluid can be expressed in terms of interior products of current 4-vectors with exterior derivatives of the appropriate 4-momentum 1-forms (whose role is central in this approach) in a fully covariant standard form whose structure is identical in the Newtonian case to that of the corresponding equation for the case of (special or general) relativistic perfect fluid mechanics. In addition to space–time covariance, this standard form exhibits chemical covariance in the sense that it is manifestly invariant under redefinition of the number densities of the independent conserved chemical constituents in terms of linear combinations of each other. It is shown how, in the strictly conservative case when no chemical reactions occur, this standard form, can be used (via the construction of suitably generalized Clebsch potentials) for setting up an Eulerian (fixed-point) variation principle in a form that is simultaneously valid for both Newtonian and relativistic cases.

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