Spin-2 particles in gravitational fields
... and the collision takes place at the origin of the coordinates. The metric (V.1) has a singularity at x2 = x3 = 0. More complete treatments of this problem show that this is a curvature singularity [17, 18, 19, 20]. From the phase we have derived the geometrical optics of the particles and verified ...
... and the collision takes place at the origin of the coordinates. The metric (V.1) has a singularity at x2 = x3 = 0. More complete treatments of this problem show that this is a curvature singularity [17, 18, 19, 20]. From the phase we have derived the geometrical optics of the particles and verified ...
Semester 1 Closure
... 7) Name the transformation(s) that are not isometric. Justify your answer. A dilation is not isometric because the side lengths are not the same- does not preserve size. (Figures are isometric if the pre-image and images are congruent- same shape AND size.) 8) Using transformations show that a||b. ...
... 7) Name the transformation(s) that are not isometric. Justify your answer. A dilation is not isometric because the side lengths are not the same- does not preserve size. (Figures are isometric if the pre-image and images are congruent- same shape AND size.) 8) Using transformations show that a||b. ...
An Introduction to Quantum Cosmology
... Quantum cosmology does not pertain to provide a complete, fundamental description of the universe, but rather provide a predictive guide for theories that do. It is a framework, based on quantized Einstein gravity or quantum geometrodynamics, in which the universe may be described as a closed quantu ...
... Quantum cosmology does not pertain to provide a complete, fundamental description of the universe, but rather provide a predictive guide for theories that do. It is a framework, based on quantized Einstein gravity or quantum geometrodynamics, in which the universe may be described as a closed quantu ...
7. THE EARLY UNIVERSE These chapters are from the book
... The difference between (2.1.9) and (2.1.10) can be understood quite straightforwardly if one considers a comoving box containing, say, N particles. Let us assume that, as the box expands, particles are neither created nor destroyed. If the particles are non-relativistic (i.e. if the box contains ‘dus ...
... The difference between (2.1.9) and (2.1.10) can be understood quite straightforwardly if one considers a comoving box containing, say, N particles. Let us assume that, as the box expands, particles are neither created nor destroyed. If the particles are non-relativistic (i.e. if the box contains ‘dus ...
Computing with Atoms and Molecules
... satisfied by using spins which are sufficiently isolated from the environment, and requirement 2 can be satisfied by using the naturally occurring magnetic interactions between spins. Unfortunately, it is difficult to initialize and read out the quantum states in a molecule, and this system cannot r ...
... satisfied by using spins which are sufficiently isolated from the environment, and requirement 2 can be satisfied by using the naturally occurring magnetic interactions between spins. Unfortunately, it is difficult to initialize and read out the quantum states in a molecule, and this system cannot r ...
Introduction to Wave Mechanics
... . Around the turn of the last century it was noticed that certain experiments on atomic systems could not be understood using classical physics. Instead, new theories were required. This led to the creation of quantum theory. There are really two quantum theories. “Old quantum theory” (pre-1925) w ...
... . Around the turn of the last century it was noticed that certain experiments on atomic systems could not be understood using classical physics. Instead, new theories were required. This led to the creation of quantum theory. There are really two quantum theories. “Old quantum theory” (pre-1925) w ...
The Ideal Gas on the Canonical Ensemble
... The first term on the r.h.s corresponds to all terms on the l.h.s for which both molecules are in the same state, the second term corresponds to the molecules being in different states. We can now see the problem. When the particles are in different state, we have counted each state twice. The state ...
... The first term on the r.h.s corresponds to all terms on the l.h.s for which both molecules are in the same state, the second term corresponds to the molecules being in different states. We can now see the problem. When the particles are in different state, we have counted each state twice. The state ...
GAP Optique Geneva University
... 1. All measurement outcomes are determined by the state of the physical system. In other words, at any time all physical quantities have their value somehow written in the physical system (these may change as time passes). 2. All measurement outcome probabilities are determined by the state of the p ...
... 1. All measurement outcomes are determined by the state of the physical system. In other words, at any time all physical quantities have their value somehow written in the physical system (these may change as time passes). 2. All measurement outcome probabilities are determined by the state of the p ...
Renormalization group
In theoretical physics, the renormalization group (RG) refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales. In particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle (cf. Compton wavelength).A change in scale is called a ""scale transformation"". The renormalization group is intimately related to ""scale invariance"" and ""conformal invariance"", symmetries in which a system appears the same at all scales (so-called self-similarity). (However, note that scale transformations are included in conformal transformations, in general: the latter including additional symmetry generators associated with special conformal transformations.)As the scale varies, it is as if one is changing the magnifying power of a notional microscope viewing the system. In so-called renormalizable theories, the system at one scale will generally be seen to consist of self-similar copies of itself when viewed at a smaller scale, with different parameters describing the components of the system. The components, or fundamental variables, may relate to atoms, elementary particles, atomic spins, etc. The parameters of the theory typically describe the interactions of the components. These may be variable ""couplings"" which measure the strength of various forces, or mass parameters themselves. The components themselves may appear to be composed of more of the self-same components as one goes to shorter distances.For example, in quantum electrodynamics (QED), an electron appears to be composed of electrons, positrons (anti-electrons) and photons, as one views it at higher resolution, at very short distances. The electron at such short distances has a slightly different electric charge than does the ""dressed electron"" seen at large distances, and this change, or ""running,"" in the value of the electric charge is determined by the renormalization group equation.