scholarly journals POSITION OPERATORS AND CENTER-OF-MASS: NEW PERSPECTIVES

2013 ◽  
Vol 28 (29) ◽  
pp. 1350146 ◽  
Author(s):  
P. AGUILAR ◽  
C. CHRYSSOMALAKOS ◽  
H. HERNANDEZ CORONADO ◽  
E. OKON
Keyword(s):  
Special Relativity ◽  
Poisson Bracket ◽  
Ad Hoc ◽  
Center Of Mass ◽  
Space Time ◽  
Noncommutative Space ◽  
Curved Space ◽  
New Criteria ◽  
Relativistic Particles ◽  
Rule Out

After reviewing the work of Pryce on Center-of-Mass (CoM) definitions in special relativity, and that of Jordan and Mukunda on position operators for relativistic particles with spin, we propose two new criteria for a CoM candidate: associativity, and compatibility with the Poisson bracket structure. We find that they are not satisfied by all of Pryce's definitions, and they also rule out Dixon's CoM generalization to the curved space–time case. We also emphasize that the various components of the CoM position do not commute among themselves, in the general case, and thus provide a natural entry point to the arena of noncommutative space–time, without the ad-hoc assumptions of the standard paradigm.

SOME CONSEQUENCES OF BORN'S RECIPROCAL RELATIVITY IN PHASE-SPACES

2011 ◽  
Vol 26 (21) ◽  
pp. 3653-3678 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
General Relativity ◽  
Time Delay ◽  
Phase Space ◽  
Special Relativity ◽  
Space Time ◽  
Relativity Theory ◽  
Relative Rotation ◽  
General Relativity Theory ◽  
Curved Space ◽  
Energy Dependent

We explore some novel consequences of Born's reciprocal relativity theory in flat phase-space and generalize the theory to the curved space–time scenario. We provide, in particular, six specific results resulting from Born's reciprocal relativity and which are not present in special relativity. These are: momentum-dependent time delay in the emission and detection of photons; energy-dependent notion of locality; superluminal behavior; relative rotation of photon trajectories due to the aberration of light; invariance of areas-cells in phase-space and modified dispersion relations. We finalize by constructing a Born reciprocal general relativity theory in curved space–time which requires the introduction of a complex Hermitian metric, torsion and nonmetricity. The latter procedure can be extended to the curved phase-space scenario.

GRAVITY CAN BE OBSERVED IN THE ABSENCE OF CURVED SPACETIME, THUS CURVED SPACETIME IS NOT RESPONCIBLE FOR GRAVITY

2015 ◽  
Vol 8 (1) ◽  
pp. 1976-1981
Author(s):  
Casey McMahon
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Relative Position ◽  
Gravitational Force ◽  
Curved Spacetime ◽  
Relative Time ◽  
Curved Space ◽  
Spacetime Curvature ◽  
Equivalence Model ◽  
The Universe

The principle postulate of general relativity appears to be that curved space or curved spacetime is gravitational, in that mass curves the spacetime around it, and that this curved spacetime acts on mass in a manner we call gravity. Here, I use the theory of special relativity to show that curved spacetime can be non-gravitational, by showing that curve-linear space or curved spacetime can be observed without exerting a gravitational force on mass to induce motion- as well as showing gravity can be observed without spacetime curvature. This is done using the principles of special relativity in accordance with Einstein to satisfy the reader, using a gravitational equivalence model. Curved spacetime may appear to affect the apparent relative position and dimensions of a mass, as well as the relative time experienced by a mass, but it does not exert gravitational force (gravity) on mass. Thus, this paper explains why there appears to be more gravity in the universe than mass to account for it, because gravity is not the resultant of the curvature of spacetime on mass, thus the “dark matter” and “dark energy” we are looking for to explain this excess gravity doesn’t exist.

Path integrals and the solution of the Schwinger model in curved space-time

1986 ◽  
Vol 33 (8) ◽  
pp. 2262-2266 ◽  
Author(s):  
J. Barcelos-Neto ◽  
Ashok Das
Keyword(s):  
Path Integrals ◽  
Space Time ◽  
Curved Space ◽  
Schwinger Model

scholarly journals GENERALIZED W3-STRINGS FROM FREE FIELDS

1995 ◽  
Vol 10 (06) ◽  
pp. 515-524 ◽  
Author(s):  
J. M. FIGUEROA-O'FARRILL ◽  
C. M. HULL ◽  
L. PALACIOS ◽  
E. RAMOS
Keyword(s):  
Bosonic Strings ◽  
Free Field ◽  
Space Time ◽  
General Construction ◽  
Special Cases ◽  
Free Fields ◽  
Rule Out ◽  
General Conditions ◽  
String Theories

The conventional quantization of w3-strings gives theories which are equivalent to special cases of bosonic strings. We explore whether a more general quantization can lead to new generalized W3-string theories by seeking to construct quantum BRST charges directly without requiring the existence of a quantum W3-algebra. We study W3-like strings with a direct space-time interpretation — that is, with matter given by explicit free field realizations. Special emphasis is placed on the attempt to construct a quantum W-string associated with the magic realizations of the classical w3-algebra. We give the general conditions for the existence of W3-like strings, and comment on how the known results fit into our general construction. Our results are negative: we find no new consistent string theories, and in particular rule out the possibility of critical strings based on the magic realizations.

scholarly journals ε-EXPANSION IN QUANTUM FIELD THEORY IN CURVED SPACE–TIME

1998 ◽  
Vol 13 (16) ◽  
pp. 2857-2874
Author(s):  
IVER H. BREVIK ◽  
HERNÁN OCAMPO ◽  
SERGEI ODINTSOV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Space Time ◽  
Quantum Field ◽  
Curved Space ◽  
Njl Model ◽  
Effective Lagrangian ◽  
Special Solutions ◽  
Curvature Approximation ◽  
Symmetric Phase

We discuss ε-expansion in curved space–time for asymptotically free and asymptotically nonfree theories. The existence of stable and unstable fixed points is investigated for fϕ4 theory and SU(2) gauge theory. It is shown that ε-expansion maybe compatible with aysmptotic freedom on special solutions of the RG equations in a special ase (supersymmetric theory). Using ε-expansion RG technique, the effective Lagrangian for covariantly constant gauge SU(2) field and effective potential for gauged NJL model are found in (4-ε)-dimensional curved space (in linear curvature approximation). The curvature-induced phase transitions from symmetric phase to asymmetric phase (chromomagnetic vacuum and chiral symmetry broken phase, respectively) are discussed for the above two models.

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