scholarly journals First-order discrete Faddeev gravity at strongly varying fields

2017 ◽  
Vol 32 (35) ◽  
pp. 1750181
Author(s):  
V. M. Khatsymovsky
Keyword(s):  
Dimensional Space ◽  
Tetrad Field ◽  
First Order ◽  
Antiferromagnetic Structure ◽  
Riemannian Connection ◽  
Order Representation ◽  
Independent Variable ◽  
The Continuum ◽  
Elementary Area ◽  
Classical Background

We consider the Faddeev formulation of general relativity (GR), which can be characterized by a kind of d-dimensional tetrad (typically d = 10) and a non-Riemannian connection. This theory is invariant w.r.t. the global, but not local, rotations in the d-dimensional space. There can be configurations with a smooth or flat metric, but with the tetrad that changes abruptly at small distances, a kind of “antiferromagnetic” structure. Previously, we discussed a first-order representation for the Faddeev gravity, which uses the orthogonal connection in the d-dimensional space as an independent variable. Using the discrete form of this formulation, we considered the spectrum of (elementary) area. This spectrum turns out to be physically reasonable just on a classical background with large connection like rotations by [Formula: see text], that is, with such an “antiferromagnetic” structure. In the discrete first-order Faddeev gravity, we consider such a structure with periodic cells and large connection and strongly changing tetrad field inside the cell. We show that this system in the continuum limit reduces to a generalization of the Faddeev system. The action is a sum of related actions of the Faddeev type and is still reduced to the GR action.

On Conformally Covariant Spinor Field Equations

1972 ◽  
Vol 50 (18) ◽  
pp. 2100-2104 ◽  
Author(s):  
Mark S. Drew
Keyword(s):  
Minkowski Space ◽  
Invariant Mass ◽  
Spinor Field ◽  
Dimensional Space ◽  
Flat Space ◽  
Field Equations ◽  
First Order ◽  
Conformally Invariant ◽  
Spinor Fields

Conformally covariant equations for free spinor fields are determined uniquely by carrying out a descent to Minkowski space from the most general first-order rotationally covariant spinor equations in a six-dimensional flat space. It is found that the introduction of the concept of the "conformally invariant mass" is not possible for spinor fields even if the fields are defined not only on the null hyperquadric but over the entire manifold of coordinates in six-dimensional space.

scholarly journals Particles, conformal invariance and criticality in pure and disordered systems

2021 ◽  
Vol 94 (3) ◽  
Author(s):  
Gesualdo Delfino
Keyword(s):  
Conformal Invariance ◽  
Disordered Systems ◽  
Short Range ◽  
Recent Progress ◽  
Quenched Disorder ◽  
Exact Methods ◽  
Special Position ◽  
Infinite Dimensional ◽  
First Order ◽  
The Continuum

AbstractThe two-dimensional case occupies a special position in the theory of critical phenomena due to the exact results provided by lattice solutions and, directly in the continuum, by the infinite-dimensional character of the conformal algebra. However, some sectors of the theory, and most notably criticality in systems with quenched disorder and short-range interactions, have appeared out of reach of exact methods and lacked the insight coming from analytical solutions. In this article, we review recent progress achieved implementing conformal invariance within the particle description of field theory. The formalism yields exact unitarity equations whose solutions classify critical points with a given symmetry. It provides new insight in the case of pure systems, as well as the first exact access to criticality in presence of short range quenched disorder. Analytical mechanisms emerge that in the random case allow the superuniversality of some critical exponents and make explicit the softening of first-order transitions by disorder.Graphic abstract

DIFFERENTIAL EQUATIONS IN A HYPERCOMPLEX SYSTEM

2020 ◽  
Vol 69 (1) ◽  
pp. 7-11
Author(s):  
A.K. Abirov ◽  
◽  
N.K. Shazhdekeeva ◽  
T.N. Akhmurzina ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Inhomogeneous System ◽  
Homogeneous Solutions ◽  
First Order ◽  
Zero Divisors ◽  
Hypercomplex System ◽  
Independent Variable ◽  
The Right

The article considers the problem of solving an inhomogeneous first-order differential equation with a variable with a constant coefficient in a hypercomplex system. The structure of the solution in different cases of the right-hand side of the differential equation is determined. The structure of solving the equation in the case of the appearance of zero divisors is shown. It turns out that when the component of a hypercomplex function is a polynomial of an independent variable, the differential equation turns into an inhomogeneous system of real variables from n equations and its solution is determined by certain methods of the theory of differential equations. Thus, obtaining analytically homogeneous solutions of inhomogeneous differential equations in a hypercomplex system leads to an increase in the efficiency of modeling processes in various fields of science and technology.

scholarly journals The X-Ray Nova GRO J0422+32 in Decline and Quiescence

1996 ◽  
Vol 158 ◽  
pp. 399-400
Author(s):  
M. R. Garcia ◽  
P. J. Callanan ◽  
J. E. McClintock ◽  
P. Zhao
Keyword(s):  
Emission Line ◽  
Emission Region ◽  
Dwarf Novae ◽  
X Ray ◽  
First Order ◽  
Band Emission ◽  
Line Region ◽  
Hα Emission ◽  
The Stability ◽  
The Continuum

We have followed the X-ray nova GRO J0422+32, spectroscopically and photometrically, throughout the decline to quiescence.In the final stages of decay (days 430…880 after the outburst, see Callanan et al. (1995) for the epoch 1995), the equivalent width (EW) of the Hα emission increases monotonically and the R magnitude decreases monotonically. This suggests that the flux in the Hα line is constant, while the continuum fades. The Hα flux is the product of the R band flux (F(R), arbitrarily scaled to 100 at R = 19 mag) and the EW, and is shown in the last column of the table below. The Hα flux varies by only ~ 30% while the continuum fades by a factor of eight (from R = 19 mag to R = 21.3 mag). So, to first order, the Hα luminosity is constant in the final stages of decay. While it is generally the case that the emission line EWs in individual dwarf novae also increase during the decay, the exact behavior seen in GRO J0422+32 is not what is seen for dwarf novae (on average). Using the relation between EW[Hβ] and Mv given in figure 6 of Patterson (1984), we would expect a factor of ~ 5 variation in the Hα flux during days 430…880. The stability of the Hα flux implies that somehow the emission line region is ‘disconnected’ from the continuum (R–band) emission region.

scholarly journals On a Possibly Pure Set-Theoretic Contribution to Black Hole Entropy

2019 ◽  
Vol 25 (2) ◽  
pp. 327-340 ◽  
Author(s):  
Gábor Etesi
Keyword(s):  
Black Hole ◽  
Dimensional Space ◽  
Mathematical Formulation ◽  
Black Hole Entropy ◽  
Conserved Quantities ◽  
Physical Problems ◽  
Dimensional Space Time ◽  
Flow Of Time ◽  
Time Continuum ◽  
The Continuum

Abstract Continuity as appears to us immediately by intuition (in the flow of time and in motion) differs from its current formalization, the arithmetical continuum or equivalently the set of real numbers used in modern mathematical analysis. Motivated by the known mathematical and physical problems arising from this formalization of the continuum, our aim in this paper is twofold. Firstly, by interpreting Chaitin’s variant of Gödel’s first incompleteness theorem as an inherent uncertainty or fuzziness of the arithmetical continuum, a formal set-theoretic entropy is assigned to the arithmetical continuum. Secondly, by analyzing Noether’s theorem on symmetries and conserved quantities, we argue that whenever the four dimensional space-time continuum containing a single, stationary, asymptotically flat black hole is modeled by the arithmetical continuum in the mathematical formulation of general relativity, the hidden set-theoretic entropy of this latter structure reveals itself as the entropy of the black hole (proportional to the area of its “instantaneous” event horizon), indicating that this apparently physical quantity might have a pure set-theoretic origin, too.

scholarly journals A Lattice Test of Alternative Interpretations of "Triviality" in (λΦ4)4 Theory

1997 ◽  
Vol 12 (14) ◽  
pp. 1011-1024 ◽  
Author(s):  
A. Agodi ◽  
G. Andronico ◽  
P. Cea ◽  
M. Consoli ◽  
L. Cosmai ◽  
...  
Keyword(s):  
Phase Transition ◽  
Effective Potential ◽  
Higgs Mass ◽  
Higgs Field ◽  
Alternative Interpretation ◽  
Lattice Data ◽  
First Order ◽  
Conventional Picture ◽  
The Continuum ◽  
Second Order Phase Transition

There are two physically different interpretations of "triviality" in (λΦ4)4 theories. The conventional description predicts a second-order phase transition and that the Higgs mass mh must vanish in the continuum limit if v, the physical vev is held fixed. An alternative interpretation, based on the effective potential obtained in "triviality-compatible" approximations (in which the shifted "Higgs" field h(x)≡Φ(x)-<Φ> is governed by an effective quadratic Hamiltonian) predicts a phase transition that is very weakly first-order and that mh and v are both finite, cutoff-independent quantities. To test these two alternatives, we have numerically computed the effective potential on the lattice. Three different methods were used to determine the critical bare mass for the chosen bare coupling value. All give excellent agreement with the literature value. Two different methods for obtaining the effective potential were used, as a control on the results. Our lattice data are fitted very well by the predictions of the unconventional picture, but poorly by the conventional picture.

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