Chapter 37 - Semiclassical quantization
... the action of linear evolution operators on infinite-dimensional vector spaces. In quantum mechanics the periodic orbit theory arose from studies of semi-conductors, and the unstable periodic orbits have been measured in experiments on the very paradigm of Bohr’s atom, the hydrogen atom, this time i ...
... the action of linear evolution operators on infinite-dimensional vector spaces. In quantum mechanics the periodic orbit theory arose from studies of semi-conductors, and the unstable periodic orbits have been measured in experiments on the very paradigm of Bohr’s atom, the hydrogen atom, this time i ...
Path integral approach to the heat kernel 1 Introduction
... produces the well-known ordering ambiguities in the identification of Ĥ from Hcl . In general this has to be expected since the classical limit is irreversible and one may loose information in the passage from the quantum to the classical world (for example, all h̄ dependent terms in the potential ...
... produces the well-known ordering ambiguities in the identification of Ĥ from Hcl . In general this has to be expected since the classical limit is irreversible and one may loose information in the passage from the quantum to the classical world (for example, all h̄ dependent terms in the potential ...
Stochastic semiclassical cosmological models
... It is clear from this equation that if n Þ0 the conformally flat symmetry is broken by the coupling of the scalar field. The action for the gravitational field, the Einstein-Hilbert action S EH g , needs to be corrected with a counterterm to cancel the divergencies that will come from the effective ...
... It is clear from this equation that if n Þ0 the conformally flat symmetry is broken by the coupling of the scalar field. The action for the gravitational field, the Einstein-Hilbert action S EH g , needs to be corrected with a counterterm to cancel the divergencies that will come from the effective ...
Heavy gravitons on-shell decay of the Higgs boson at high
... Background (CMB) temperature anisotropy, suggest that our Universe is essentially flat and that it consists mainly of dark matter and dark energy [15]. A theory about the origin of dark matter and dark energy is to regard them as consisting of massive gravitons. There are indications that those mass ...
... Background (CMB) temperature anisotropy, suggest that our Universe is essentially flat and that it consists mainly of dark matter and dark energy [15]. A theory about the origin of dark matter and dark energy is to regard them as consisting of massive gravitons. There are indications that those mass ...
The Road to Loop Quantum Gravity - Theoretical High
... magnitude and opposite sign to obtain a finite perturbation series. In the pertubation expansion of GRT it has been proven by Goroff and Sagnotti [1] that there are infinitely many divergences. Thus infinitely many counterterms are needed to produce any physical results. This is called the non-renor ...
... magnitude and opposite sign to obtain a finite perturbation series. In the pertubation expansion of GRT it has been proven by Goroff and Sagnotti [1] that there are infinitely many divergences. Thus infinitely many counterterms are needed to produce any physical results. This is called the non-renor ...
Derivation Of The Schwarzschild Radius Without General
... Schwarzschild in 1915. The issue was that I wanted to derive the thermodynamic properties of black holes without using any results from Einstein's General Theory of Relativity; and although, at that time, I could have included the derivation presented here, I did not do so because I wanted to write ...
... Schwarzschild in 1915. The issue was that I wanted to derive the thermodynamic properties of black holes without using any results from Einstein's General Theory of Relativity; and although, at that time, I could have included the derivation presented here, I did not do so because I wanted to write ...
What Every Physicist Should Know About String Theory
... Even though we do not really understand it, quantum gravity is supposed to be some sort of theory in which, at least from a macroscopic point of view, we average, in a quantum mechanical sense, over all possible spacetime geometries. (We do not know to what extent this description is valid microsco ...
... Even though we do not really understand it, quantum gravity is supposed to be some sort of theory in which, at least from a macroscopic point of view, we average, in a quantum mechanical sense, over all possible spacetime geometries. (We do not know to what extent this description is valid microsco ...
Plenty of Nothing: Black Hole Entropy in Induced Gravity
... number of different ways to distribute two signs + and – over the cells of Planckian size on the horizon surface. This estimation suggests that a reasonable microscopical explanation of the Bekenstein-Hawking entropy must be based on the quantum gravity, this Holy Grail of the theoretical physics. T ...
... number of different ways to distribute two signs + and – over the cells of Planckian size on the horizon surface. This estimation suggests that a reasonable microscopical explanation of the Bekenstein-Hawking entropy must be based on the quantum gravity, this Holy Grail of the theoretical physics. T ...
Seminar Quantum Field Theory - Institut für Theoretische Physik III
... amplitude stays divergent also at higher orders in perturbation theory. But fortunately due to the dependence on the number of external legs there should be a finite number of divergent scattering amplitudes. Such a QFT we call a Renormalizable Theory. Now consider the case of a spacetime with more ...
... amplitude stays divergent also at higher orders in perturbation theory. But fortunately due to the dependence on the number of external legs there should be a finite number of divergent scattering amplitudes. Such a QFT we call a Renormalizable Theory. Now consider the case of a spacetime with more ...
Analogue gravity from field theory normal modes?
... solutions) if and only if the effective metric gµν has Lorentzian signature ±[−, +d ]. Observe that if the Lagrangian contains non-trivial second derivatives you should not be too surprised to see terms beyond the d’Alembertian showing up in the linearized equations of motion. Specific examples of t ...
... solutions) if and only if the effective metric gµν has Lorentzian signature ±[−, +d ]. Observe that if the Lagrangian contains non-trivial second derivatives you should not be too surprised to see terms beyond the d’Alembertian showing up in the linearized equations of motion. Specific examples of t ...
Lectures on Topological Quantum Field Theory
... ∂([0, t]) = {t} ∪ −{0}. (The minus sign is for the orientation.) This pt for the Euclidean theory is the heat kernel of M , the probability density which measures the amount of heat which flows from x to y in time t. If H : F(M ) → F(M ) is the Laplace operator we can write this heat operator as ...
... ∂([0, t]) = {t} ∪ −{0}. (The minus sign is for the orientation.) This pt for the Euclidean theory is the heat kernel of M , the probability density which measures the amount of heat which flows from x to y in time t. If H : F(M ) → F(M ) is the Laplace operator we can write this heat operator as ...
Three principles for canonical quantum gravity - Philsci
... quantum gravity: 1) dieomorphism invariance, 2) implementing the proper dynamics and related constraint algebra, 3) local Lorentz invariance. We illustrate each of them with its role in model calculations in loop quantum gravity. ...
... quantum gravity: 1) dieomorphism invariance, 2) implementing the proper dynamics and related constraint algebra, 3) local Lorentz invariance. We illustrate each of them with its role in model calculations in loop quantum gravity. ...
Asymptotic Notation - Department of Computer Science
... that for all n large enough f(n) ≤ k.g(n) f(n) = Ω(g(n)) means k.g(n) is a lower bound on f(n). So there exists some constant k such that for all n large enough f(n) ≥ k.g(n) f(n) = Θ(g(n)) means k 1.g(n) is an upper bound on f(n) and k 2.g(n) is a lower bound on f(n). So there exist constants k 1 a ...
... that for all n large enough f(n) ≤ k.g(n) f(n) = Ω(g(n)) means k.g(n) is a lower bound on f(n). So there exists some constant k such that for all n large enough f(n) ≥ k.g(n) f(n) = Θ(g(n)) means k 1.g(n) is an upper bound on f(n) and k 2.g(n) is a lower bound on f(n). So there exist constants k 1 a ...
Mixing Transformations in Quantum Field Theory and Neutrino
... For example, in theories with spontaneous symmetry breaking the same set of Heisenberg field equations describes the normal (symmetric) phase as well as the symmetry broken phase, according to the representation one chooses for the asymptotic fields. Notice that in quantum mechanics no problem arise ...
... For example, in theories with spontaneous symmetry breaking the same set of Heisenberg field equations describes the normal (symmetric) phase as well as the symmetry broken phase, according to the representation one chooses for the asymptotic fields. Notice that in quantum mechanics no problem arise ...
Book of Abstracts
... Neutrinos qualify as a perfect probe for quantum gravity as they are unique in various ways: -Neutrino masses are often understood as a consequence of the breaking of lepton number. Such global symmetries are usually expected to be broken by quantum gravity effects. -Standard Model singlets such as ...
... Neutrinos qualify as a perfect probe for quantum gravity as they are unique in various ways: -Neutrino masses are often understood as a consequence of the breaking of lepton number. Such global symmetries are usually expected to be broken by quantum gravity effects. -Standard Model singlets such as ...
Quantum fluctuations and thermal dissipation in higher derivative
... of a massive charged (quark like) particle at the boundary. What we would essentially study is the linear response of the system when perturbed due to some external (electrical) force. In order to compute the two point correlation function, we would assume the so-called fluctuation dissipation theor ...
... of a massive charged (quark like) particle at the boundary. What we would essentially study is the linear response of the system when perturbed due to some external (electrical) force. In order to compute the two point correlation function, we would assume the so-called fluctuation dissipation theor ...
Some Notes on Field Theory
... Quantum Field Theory is a general technique for dealing with systems with an infinite number of degrees of freedom. Examples are systems of many interacting particles or critical phenomena like second order phase transitions. Here we will concentrate on the scattering of particles, but the general f ...
... Quantum Field Theory is a general technique for dealing with systems with an infinite number of degrees of freedom. Examples are systems of many interacting particles or critical phenomena like second order phase transitions. Here we will concentrate on the scattering of particles, but the general f ...
CALCULUS OF FUNCTIONALS
... series. Our practical interest in the integral aspects of the functional calculus we owe ultimately to Richard Feynman; we have seen that the Schrödinger equation provides—interpretive matters aside—a wonderful instance of a classical field, and it was Feynman who first noticed (or, at least, who firs ...
... series. Our practical interest in the integral aspects of the functional calculus we owe ultimately to Richard Feynman; we have seen that the Schrödinger equation provides—interpretive matters aside—a wonderful instance of a classical field, and it was Feynman who first noticed (or, at least, who firs ...
Renormalization Group Flows for Quantum Gravity
... Asymptotic Safety (Weinberg, Reuter, Percacci, Saueressig...): searches for a non-trivial ultraviolet fixed point in the theory space of all diffeo-invariant functions of the metric. Uses mostly numerical tools. No background independence (no sum over topologies). Tensor Models (Gurau, Ben Geloun, B ...
... Asymptotic Safety (Weinberg, Reuter, Percacci, Saueressig...): searches for a non-trivial ultraviolet fixed point in the theory space of all diffeo-invariant functions of the metric. Uses mostly numerical tools. No background independence (no sum over topologies). Tensor Models (Gurau, Ben Geloun, B ...
Gravity Duals for Nonrelativistic Conformal Field Theories Please share
... system. In general, physics in the far infrared is described by a (sometimes trivial) fixed point of the renormalization group. It has been argued that the associated zerotemperature CFT controls a swath of the finite-temperature phase diagram, namely, the region in which the temperature is the only ...
... system. In general, physics in the far infrared is described by a (sometimes trivial) fixed point of the renormalization group. It has been argued that the associated zerotemperature CFT controls a swath of the finite-temperature phase diagram, namely, the region in which the temperature is the only ...
Non-relativistic Holography and Renormalization
... 2. Perform calculations of physical processes using the bare quantities at any required order in perturbation theory 3. Finally fix the parameter (or parameters for that matter) to reproduce and/or predict experimental results. A theory that is ill-defined however, suggests that F needs to be repara ...
... 2. Perform calculations of physical processes using the bare quantities at any required order in perturbation theory 3. Finally fix the parameter (or parameters for that matter) to reproduce and/or predict experimental results. A theory that is ill-defined however, suggests that F needs to be repara ...
Gravity as the breakdown of conformal invariance
... model. We found that in an appropriate frame, and for γ = 2, three things happen concurrently: i) UV dimensional reduction to two, ii) gravity conformally coupled to all particles, and iii) pervasive scale invariance. In work in preparation [12] we have part-generalized this result, proving that in ...
... model. We found that in an appropriate frame, and for γ = 2, three things happen concurrently: i) UV dimensional reduction to two, ii) gravity conformally coupled to all particles, and iii) pervasive scale invariance. In work in preparation [12] we have part-generalized this result, proving that in ...
GeoSym-QFT
... gravity as the geometry of spacetime. The unification of the two is the present challenge, and it will probably require a change of paradigm with the introduction of innovative concepts and tools. The title of our project: Geometry and Symmetry in Quantum Field Theory, tries to resume in few words a ...
... gravity as the geometry of spacetime. The unification of the two is the present challenge, and it will probably require a change of paradigm with the introduction of innovative concepts and tools. The title of our project: Geometry and Symmetry in Quantum Field Theory, tries to resume in few words a ...
The Dimensions of M
... singularity is cloaked by the surface of an event horizon. That is, any information which is only deciphered by a quantum theory of gravitation might be locked away within the black hole, never making contact with the outside universe. However, as briefly mentioned above, even at the semi-classical ...
... singularity is cloaked by the surface of an event horizon. That is, any information which is only deciphered by a quantum theory of gravitation might be locked away within the black hole, never making contact with the outside universe. However, as briefly mentioned above, even at the semi-classical ...
GS 388 handout: Gravity Anomalies: brief summary 1 1. Observed
... 1. Observed gravity is measured at a point of observation (Lat., Long., elevation) and is generally a measurement of the difference between the gravity at the point of observation and the gravity at one of the bench marks in a world-wide or national gravity network. These benchmarks have been tied ( ...
... 1. Observed gravity is measured at a point of observation (Lat., Long., elevation) and is generally a measurement of the difference between the gravity at the point of observation and the gravity at one of the bench marks in a world-wide or national gravity network. These benchmarks have been tied ( ...