HOLOMORPHIC QUANTUM MECHANICS, CONFORMAL REFLECTION AND THE INTERNAL SYMMETRY OF HADRONS

1989 ◽  
Vol 04 (17) ◽  
pp. 4449-4467 ◽  
Author(s):  
PRATUL BANDYOPADHYAY
Keyword(s):  
Quantum Mechanics ◽  
Minkowski Space ◽  
Composite System ◽  
Conformal Geometry ◽  
Reflection Group ◽  
Internal Symmetry ◽  
Space Time ◽  
Internal Space ◽  
Minkowski Space Time ◽  
Antiparticle State

It is shown here that the holomorphic quantum mechanics in a complexified Minkowski space-time helps us to study the geometrical feature of the internal space of a particle and its relevance with conformal geometry. It is noted that the conformal reflection can be depicted in the formalism of an internal helicity which takes the value [Formula: see text] and [Formula: see text] for the particle and antiparticle state. This again can be described in the framework of holomorphic quantum mechanics in terms of the half-orbital angular momentum of a constituent in an anisotropic space in the sense of Minkowski space-time with a fixed lz value for the particle and antiparticle configuration when a composite system is considered. A massive or massless spinor moving with such characteristic in the configuration of a composite system can be depicted as a Cartan semispinor and behaves as a twistor. The doublet of such spinors with opposite helicities represent an eight-component conformal spinor. The internal symmetry group SU(3) for a composite system of hadrons can then be realized from the reflection group. This formalism reveals the microlocal region of a complexified Minkowski space-time as a twistor space.

TWISTOR GEOMETRY, SPINOR STRUCTURE AND NATURE OF SUPERSPACE

1989 ◽  
Vol 04 (05) ◽  
pp. 1111-1123 ◽  
Author(s):  
PRATUL BANDYOPADHYAY ◽  
PRADIP GHOSH
Keyword(s):  
Minkowski Space ◽  
Reflection Group ◽  
Internal Symmetry ◽  
Space Time ◽  
Base Space ◽  
Internal Space ◽  
Direction Vector ◽  
Spinor Structure ◽  
Minkowski Space Time ◽  
Time Point

The nature of superspace is studied here from the viewpoint of eight-component conformal spinors which can be split into two Cartan semispinors having two internal helicities corresponding to particle and anti-particle states. This leads to the generation of internal symmetry through reflection group. It is shown that each member of the doublet can be taken to behave as twistors in complexified Minkowski space-time. This helps us to introduce a spinor structure at each space-time point and the spinor coordinate gives rise to the internal helicity. This may be achieved through the introduction of a direction vector attached to each space-time point. Superspace here appears as a bundle space where the base space is the ordinary Minkowski space-time and the spinorial coordinates generated through the introduction of the direction vector from the fibre. This suggests that the internal space of hadrons is anisotropic in nature.

scholarly journals Testing quantum mechanics in non-Minkowski space-time with high power lasers and 4th generation light sources

2012 ◽  
Vol 2 (1) ◽  
Author(s):  
B. J. B. Crowley ◽  
R. Bingham ◽  
R. G. Evans ◽  
D. O. Gericke ◽  
O. L. Landen ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Minkowski Space ◽  
High Power ◽  
Space Time ◽  
Light Sources ◽  
High Power Lasers ◽  
Minkowski Space Time

scholarly journals Non-inertial frames in Minkowski space-time, accelerated either mathematical or dynamical observers and comments on non-inertial relativistic quantum mechanics

2014 ◽  
Vol 11 (10) ◽  
pp. 1450086 ◽  
Author(s):  
Horace W. Crater ◽  
Luca Lusanna
Keyword(s):  
Quantum Mechanics ◽  
Minkowski Space ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Minkowski Space Time ◽  
Accelerated Observers ◽  
Inertial Frames ◽  
Locality Principle

After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz transformations as suggested by the locality principle. These non-inertial frames have non-Euclidean 3-spaces and contain the differentially rotating ones in Euclidean 3-spaces as a subcase. Then we discuss how to replace mathematical accelerated observers with dynamical ones (their world-lines belong to interacting particles in an isolated system) and how to define Unruh–DeWitt detectors without using mathematical Rindler uniformly accelerated observers. Also some comments are done on the transition from relativistic classical mechanics to relativistic quantum mechanics in non-inertial frames.

scholarly journals Quantum Statistics in Cylindrical Time-evolution of Electrons and Physical Reality

2020 ◽  
Vol 36 (3) ◽  
Author(s):  
Vo Van Thuan ◽  
Dao Dinh Duc
Keyword(s):  
Quantum Mechanics ◽  
Plane Wave ◽  
Minkowski Space ◽  
Time Evolution ◽  
Physical Reality ◽  
Space Time ◽  
Quantum Mechanical ◽  
Minkowski Space Time ◽  
Short Time ◽  
Physical Quantities

Due to helical cylindrical time-evolution of electrons the mankind observation at a quantum mechanical scale depends on synchronization between observers and their surrounding cosmological medium by collective dynamics. From one side, the synchronization leads to linearization of an embedded 4D space-time reminiscent of the flat Minkowski space-time. From another side, variation of the synchronization due to independent proper plane wave oscillations of each electron being constrained in a short time quantized period, implies that there only statistical averaged physical quantities are observable, which is in consistency with statistical indeterministic concept of traditional quantum mechanics.

scholarly journals Vacuum thermal effects in flat space-time from conformal quantum mechanics

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Michele Arzano
Keyword(s):  
Quantum Mechanics ◽  
Minkowski Space ◽  
Time Evolution ◽  
Time Domain ◽  
Thermal Effects ◽  
Proper Time ◽  
Space Time ◽  
Theoretical Derivation ◽  
Minkowski Space Time ◽  
Conformal Quantum Mechanics

Abstract The generators of radial conformal symmetries in Minkowski space-time can be mapped to the generators of time evolution in conformal quantum mechanics. Within this correspondence we show that in conformal quantum mechanics the state associated to the inertial vacuum in Minkowski space-time has the structure of a thermofield double. Such state is built from a bipartite “vacuum state”, the ground state of the generators of hyperbolic time evolution, which cover only part of the time domain. When time evolution is restricted to a finite time domain one obtains the temperature perceived by static diamond observers in the Minkowski vacuum. When time evolution is determined by dilations, covering only half of the time line, the temperature of the thermofield double corresponds to the non-vanishing temperature perceived by Milne observers whose proper time evolution is confined to the future cone (Milne universe) of Minkowski space-time. The two pictures are related by a conformal transformation on the real line. Our result provides a purely group theoretical derivation of the Milne and diamond temperatures and shows that the fundamental ingredient for vacuum thermal effects is the presence of a horizon rather than acceleration.

scholarly journals SPINOR GEOMETRY

2012 ◽  
Vol 27 (22) ◽  
pp. 1250126 ◽  
Author(s):  
A. NICOLAIDIS ◽  
V. KIOSSES
Keyword(s):  
Quantum Mechanics ◽  
String Theory ◽  
Minkowski Space ◽  
Conformal Symmetry ◽  
Space Time ◽  
Large Network ◽  
Dirac Spinor ◽  
Minkowski Space Time ◽  
Spinor Geometry ◽  
Relational Logic

It has been proposed that quantum mechanics and string theory share a common inner syntax, the relational logic of C. S. Peirce. Along this line of thought we consider the relations represented by spinors. Spinor composition leads to the emergence of Minkowski space–time. Inversely, the Minkowski space–time is istantiated by the Weyl spinors, while the merger of two Weyl spinors gives rise to a Dirac spinor. Our analysis is applied also to the string geometry. The string constraints are represented by real spinors, which create a parametrization of the string worldsheet identical to the Enneper–Weierstass representation of minimal surfaces. Further, a spinorial study of the AdS3 space–time reveals a Hopf fibration AdS3 → AdS2. The conformal symmetry inherent in AdS3 is pointed out. Our work indicates the hidden ties between logic-quantum mechanics-string theory-geometry and vindicates the Wheeler's proposal of pregeometry as a large network of logical propositions.

On generalized partially null Mannheim curves in Minkowski space-time

2016 ◽  
Vol 46 (1) ◽  
pp. 159-170 ◽  
Author(s):  
Emilija Nešović ◽  
Milica Grbović
Keyword(s):  
Minkowski Space ◽  
Space Time ◽  
Minkowski Space Time

scholarly journals A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

2007 ◽  
Vol 16 (06) ◽  
pp. 1027-1041 ◽  
Author(s):  
EDUARDO A. NOTTE-CUELLO ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Gravitational Theory ◽  
Space Time ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Yang Mills ◽  
Minkowski Space Time ◽  
Clifford Bundle ◽  
Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

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