The Complex Geometry of the Natural World
... Moreover, it is envisaged that when the space-time is curved, or endowed with an electromagnetic field, or a more general gauge field, [8], the twistor space should acquire a more complicated complex structure than that of C4. Some considerable successes have been achieved, as it turns out, using th ...
... Moreover, it is envisaged that when the space-time is curved, or endowed with an electromagnetic field, or a more general gauge field, [8], the twistor space should acquire a more complicated complex structure than that of C4. Some considerable successes have been achieved, as it turns out, using th ...
Transformation properties of the Lagrange function
... Three points about this example are important to be noticed: (a) the transformation (9) satisfies the second order condition for the system (8), but not necessarily for any Lagrange equation; as a counterexample the free particle equation q̈ = 0 is sufficient; (b) besides the different functional fo ...
... Three points about this example are important to be noticed: (a) the transformation (9) satisfies the second order condition for the system (8), but not necessarily for any Lagrange equation; as a counterexample the free particle equation q̈ = 0 is sufficient; (b) besides the different functional fo ...
A Rough Guide to Quantum Chaos
... states that in certain classical limits, quantum theory should reproduce the predictions of classical theory with vanishing errors. In particular, for those objects which are known to be in excellent agreement with classical mechanics — chairs, planets, etc. — quantum effects should be negligible. I ...
... states that in certain classical limits, quantum theory should reproduce the predictions of classical theory with vanishing errors. In particular, for those objects which are known to be in excellent agreement with classical mechanics — chairs, planets, etc. — quantum effects should be negligible. I ...
Statistical Thermodynamics. Objectives of the Theory
... Macroscopic systems exhibit three important properties (features) distinguishing them from microscopic systems: 1. In macroscopic systems occur irreversible processes leading to equilibrium states in which the properties of the system do not depend on time (and there are no mass flows). 2. The equil ...
... Macroscopic systems exhibit three important properties (features) distinguishing them from microscopic systems: 1. In macroscopic systems occur irreversible processes leading to equilibrium states in which the properties of the system do not depend on time (and there are no mass flows). 2. The equil ...
Doctoral Programmes in Physics at IMSc
... Detailed syllabi of the proposed course The course contents are indicative and will be fine tuned with experience. ...
... Detailed syllabi of the proposed course The course contents are indicative and will be fine tuned with experience. ...
Time in quantum mechanics
... distinguished. Quite often the coordinates of space and the position variables of a point particle are denoted by the same symbols x, y, z (e.g. when one writes ψ(x, y, z, t) for the wave function of a particle). To avoid this confusion we shall denote the dynamical position variables of a particle ...
... distinguished. Quite often the coordinates of space and the position variables of a point particle are denoted by the same symbols x, y, z (e.g. when one writes ψ(x, y, z, t) for the wave function of a particle). To avoid this confusion we shall denote the dynamical position variables of a particle ...
Quantum Gravity: the view from particle physics
... describe the physical degrees of freedom also at the very smallest distances. The first attempt of quantizing gravity relied on canonical quantization, with the spatial metric components and their conjugate momenta as the canonical variables, and the Wheeler-DeWitt equation governing the dynamics [3 ...
... describe the physical degrees of freedom also at the very smallest distances. The first attempt of quantizing gravity relied on canonical quantization, with the spatial metric components and their conjugate momenta as the canonical variables, and the Wheeler-DeWitt equation governing the dynamics [3 ...
COVARIANT HAMILTONIAN GENERAL RELATIVITY
... variations in the 1930’s. In section 2, I briefly illustrate the main lines of this formulation using the example of a scalar field, and I discuss its relation with the relativistic notions of state and observable considered in Ref. 1 I then apply these ideas to general relativity (GR) in Section 3. ...
... variations in the 1930’s. In section 2, I briefly illustrate the main lines of this formulation using the example of a scalar field, and I discuss its relation with the relativistic notions of state and observable considered in Ref. 1 I then apply these ideas to general relativity (GR) in Section 3. ...
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... in the modern theoretical physics of quantum gravity, topological field theory, and conformal field theory. The spin-off from his twistor theory and his early attempts at quantum geometry is significant. Penrose's original spin networks for SU(2) have been extended to any Lie group G even to categor ...
... in the modern theoretical physics of quantum gravity, topological field theory, and conformal field theory. The spin-off from his twistor theory and his early attempts at quantum geometry is significant. Penrose's original spin networks for SU(2) have been extended to any Lie group G even to categor ...
Quantum gravitational contributions to quantum electrodynamics
... The potential importance of the original calculation 13 stimulated a number of further investigations that cast doubt on its findings. It was shown 15 that a different choice of gauge condition led to the absence of any quantum gravity correction to the Yang-Mills β-function. Because of the possible ...
... The potential importance of the original calculation 13 stimulated a number of further investigations that cast doubt on its findings. It was shown 15 that a different choice of gauge condition led to the absence of any quantum gravity correction to the Yang-Mills β-function. Because of the possible ...