Physics 217: The Renormalization Group Winter 2016 Lecturer: McGreevy Last updated: 2016/03/10, 15:55:16
... As a practical physicist, why should you care about this result? Here’s one kind of answer: suppose you have in your hands some object which is locally one-dimensional, but squiggles around in a seemingly random way. It is governed by some microscopic dynamics which are mysterious to you, and you wo ...
... As a practical physicist, why should you care about this result? Here’s one kind of answer: suppose you have in your hands some object which is locally one-dimensional, but squiggles around in a seemingly random way. It is governed by some microscopic dynamics which are mysterious to you, and you wo ...
generalized twist-deformed rindler space-times
... counterpart of Rindler space - so-called (linearized) κ - Rindler space and twistdeformed Rindler spacetime, respectively. First of them is associated with the wellknown κ - deformed Minkowski space [9], [10]2, while the second one with twisted canonical, Lie-algebraic and quadratic quantum Minkowsk ...
... counterpart of Rindler space - so-called (linearized) κ - Rindler space and twistdeformed Rindler spacetime, respectively. First of them is associated with the wellknown κ - deformed Minkowski space [9], [10]2, while the second one with twisted canonical, Lie-algebraic and quadratic quantum Minkowsk ...
Geometric constructions for repulsive gravity and
... In this thesis we present two geometric theories designed to extend general relativity. It can be seen as one of the aims of such theories to model the observed accelerating expansion of the universe as a gravitational phenomenon, or to provide a mathematical structure for the formulation of quantum ...
... In this thesis we present two geometric theories designed to extend general relativity. It can be seen as one of the aims of such theories to model the observed accelerating expansion of the universe as a gravitational phenomenon, or to provide a mathematical structure for the formulation of quantum ...
Quantum computation of scattering in scalar quantum field theories
... The simplicity of φ4 theory makes it suitable for studying challenging formal aspects of quantum field theory. The existence of the φ4 continuum theory has been rigorously established in two [47–51] and three [52, 53] (spacetime) dimensions. The perturbative expansion for the scattering matrix has b ...
... The simplicity of φ4 theory makes it suitable for studying challenging formal aspects of quantum field theory. The existence of the φ4 continuum theory has been rigorously established in two [47–51] and three [52, 53] (spacetime) dimensions. The perturbative expansion for the scattering matrix has b ...
Introduction to Loop Quantum Gravity and Spin Foams
... of the standard model to situations where a non trivial, but weak, gravitational field is present. These situations are thought to be those where the spacetime curvature is small in comparison with the Planck scale, although a clear justification for its regime of validity in strong gravitational fi ...
... of the standard model to situations where a non trivial, but weak, gravitational field is present. These situations are thought to be those where the spacetime curvature is small in comparison with the Planck scale, although a clear justification for its regime of validity in strong gravitational fi ...
Renormalization and quantum field theory
... The justification for this rather mysterious definition is Theorem 15, which shows that renormalizations act simply transitively on the Feynman measures associated to a given local cut propagator. In other words, although there is no canonical ...
... The justification for this rather mysterious definition is Theorem 15, which shows that renormalizations act simply transitively on the Feynman measures associated to a given local cut propagator. In other words, although there is no canonical ...
Possible large-N fixed-points and naturalness for O(N) scalar fields
... mechanics of magnets, the Gaussian fixed point (GFP) controls high-energy behavior while the lower-energy dynamics is governed by a crossover to the non-trivial Wilson–Fisher fixed point (WFP) [7]. However, the situation in 4D massive λφ 4 theory, the simplest (but unconfirmed) model for W ± , Z mas ...
... mechanics of magnets, the Gaussian fixed point (GFP) controls high-energy behavior while the lower-energy dynamics is governed by a crossover to the non-trivial Wilson–Fisher fixed point (WFP) [7]. However, the situation in 4D massive λφ 4 theory, the simplest (but unconfirmed) model for W ± , Z mas ...
Quantum Gravity on $ dS_ {3} $
... fixed holonomy Hb around the non-contractible cycle. This corresponds to the partition function with fixed period β of the Euclidean time, that is, fixed inverse temperature. This in turn means we are dealing with the canonical ensemble. The variable conjugate to this holonomy is the holonomy around ...
... fixed holonomy Hb around the non-contractible cycle. This corresponds to the partition function with fixed period β of the Euclidean time, that is, fixed inverse temperature. This in turn means we are dealing with the canonical ensemble. The variable conjugate to this holonomy is the holonomy around ...
Non-Perturbative Aspects of Nonlinear Sigma Models
... this solution, the mass gap of the model could be computed [45] by comparing computations of the free energy that were obtained by the thermodynamic Bethe ansatz and by perturbation theory. In constrast, nonlinear O(N ) models in d > 2 are generally considered to be only effective theories, as the co ...
... this solution, the mass gap of the model could be computed [45] by comparing computations of the free energy that were obtained by the thermodynamic Bethe ansatz and by perturbation theory. In constrast, nonlinear O(N ) models in d > 2 are generally considered to be only effective theories, as the co ...
Finite size effects in quantum field theory
... [2], the right hand side of the equation can be expressed as an infinite sum of products of Feynman propagators. Each term in the expansion can be diagrammatically represented as a Feynman diagram. Through the LSZ reduction formula the scattering matrix can be expressed in terms of a series of such ...
... [2], the right hand side of the equation can be expressed as an infinite sum of products of Feynman propagators. Each term in the expansion can be diagrammatically represented as a Feynman diagram. Through the LSZ reduction formula the scattering matrix can be expressed in terms of a series of such ...
wormholes and supersymmetry
... There are t.hree steps in this procedure that nced justifying. The first is the use of imaginary time to givc Euclidean four-spacc instead of L\)rentzian spacetime. Thcre is no r~al justification for t.his procedure, bl!t in these days when therc is no king in Israel, every one do('s what secms righ ...
... There are t.hree steps in this procedure that nced justifying. The first is the use of imaginary time to givc Euclidean four-spacc instead of L\)rentzian spacetime. Thcre is no r~al justification for t.his procedure, bl!t in these days when therc is no king in Israel, every one do('s what secms righ ...
What is the Entropy in Entropic Gravity?
... the formulation of the laws of black hole mechanics [1] and the derivation of the BekensteinHawking entropy [2, 3]. More recently, ideas such as the holographic principle [4, 5], black hole complementarity [6], the gauge/gravity correspondence [7–9], and the firewall puzzle [10, 11] have provided fu ...
... the formulation of the laws of black hole mechanics [1] and the derivation of the BekensteinHawking entropy [2, 3]. More recently, ideas such as the holographic principle [4, 5], black hole complementarity [6], the gauge/gravity correspondence [7–9], and the firewall puzzle [10, 11] have provided fu ...
Stable bounce and inflation in non-local higher derivative
... only be determined if one knows the function around a finite region surrounding the space-time point in question. This property also manifests in the way one is often able to replace the infinite differential equation of motion with an integral equation [11]. The theories however are only mildly non ...
... only be determined if one knows the function around a finite region surrounding the space-time point in question. This property also manifests in the way one is often able to replace the infinite differential equation of motion with an integral equation [11]. The theories however are only mildly non ...
E.T.WHITTAKER`S QUANTUM FORMALISM
... Near the end of that volume Whittaker departs from his self-imposed time frame to allude (at page 279) to some quantum mechanical work which he himself published in . As it happens, I had come quite by accident upon the paper in question5 in , had recognized its relevance to my then on-going ...
... Near the end of that volume Whittaker departs from his self-imposed time frame to allude (at page 279) to some quantum mechanical work which he himself published in . As it happens, I had come quite by accident upon the paper in question5 in , had recognized its relevance to my then on-going ...
Interpreting Effective Field Theories
... principle. Polchinski (1993, pg. 6) articulates such a principle in the following way: The low energy physics depends on the short distance theory only through the relevant and marginal couplings, and possibly through some leading irrelevant couplings if one measures small enough effects. (Polchinsk ...
... principle. Polchinski (1993, pg. 6) articulates such a principle in the following way: The low energy physics depends on the short distance theory only through the relevant and marginal couplings, and possibly through some leading irrelevant couplings if one measures small enough effects. (Polchinsk ...
Untitled
... an opportunity for a renormalizable theory, a better understanding of black hole entropy and perhaps even a step further along the road to a theory of everything. While there are many quantum-theoretical issues to be dealt with (Weyl anomaly, unitarity, ghosts), there are also profound obstacles for ...
... an opportunity for a renormalizable theory, a better understanding of black hole entropy and perhaps even a step further along the road to a theory of everything. While there are many quantum-theoretical issues to be dealt with (Weyl anomaly, unitarity, ghosts), there are also profound obstacles for ...
Twenty years of the Weyl anomaly
... This was the road to Damascus for Steve as far as Weyl anomalies were concerned an4 like many a recent convert, he went on to become their most ardent advocatet. This was also the beginning of a very fruitful collaboration between the two of us. The significance of my paper with Deser and Isham was ...
... This was the road to Damascus for Steve as far as Weyl anomalies were concerned an4 like many a recent convert, he went on to become their most ardent advocatet. This was also the beginning of a very fruitful collaboration between the two of us. The significance of my paper with Deser and Isham was ...
The Automorphic Universe
... hyperbolic Kac-Moody algebra HA1 and the primitive periodic orbits inside the fundamental domain of its Weyl group. ...
... hyperbolic Kac-Moody algebra HA1 and the primitive periodic orbits inside the fundamental domain of its Weyl group. ...
BARRIER PENETRATION AND INSTANTONS J. ZINN - IPhT
... at the end of section 1.1). The Euclidean formalism based on calculating the density matrix at thermal equilibrium e−βH , describes formally an evolution in imaginary time. We verify, in this chapter, that indeed it allows evaluating barrier penetration effects. Although the methods can be generaliz ...
... at the end of section 1.1). The Euclidean formalism based on calculating the density matrix at thermal equilibrium e−βH , describes formally an evolution in imaginary time. We verify, in this chapter, that indeed it allows evaluating barrier penetration effects. Although the methods can be generaliz ...
Black Hole Entropy: From Shannon to Bekenstein
... forms of quantum mechanical modes of the states inside and outside the BH horizon (see also [9]). This directly yields the probabilities of individual ingoing modes being trapped inside the BH horizon, (which is indeed unity), or tunneling out of the BH horizon and escaping to infinity to be perceiv ...
... forms of quantum mechanical modes of the states inside and outside the BH horizon (see also [9]). This directly yields the probabilities of individual ingoing modes being trapped inside the BH horizon, (which is indeed unity), or tunneling out of the BH horizon and escaping to infinity to be perceiv ...
Generalized Second Law in String Cosmology
... fate of cosmological singularities, with the expectation that singularities are smoothed and turned into brief epochs of high curvature. However, many attempts to seduce an answer out of string theory regarding cosmological singularities have failed so far, even after the wave of recent new developm ...
... fate of cosmological singularities, with the expectation that singularities are smoothed and turned into brief epochs of high curvature. However, many attempts to seduce an answer out of string theory regarding cosmological singularities have failed so far, even after the wave of recent new developm ...
Large Extra Dimensions - Are you sure you want to look at this?
... their model, the extra dimension could even be of infinite size and still reproduce our fourdimensional gravity. Thus, it was found that large extra dimensions were not only allowed theoretically, but they provided an explanation for the hierarchy problem that has been a longstanding problem in part ...
... their model, the extra dimension could even be of infinite size and still reproduce our fourdimensional gravity. Thus, it was found that large extra dimensions were not only allowed theoretically, but they provided an explanation for the hierarchy problem that has been a longstanding problem in part ...
Semi-classical formula beyond the Ehrenfest time in
... Localized regime: After that time, the coherent state spreads more and more. But its width is still of microscopic size if ∆t 1, i.e. t 12 tE . In more precise terms, the semi-classical measure of ψ (t) is still a Dirac measure at x (t) in that range of time. In our example 21 tE = 3.6. At a tim ...
... Localized regime: After that time, the coherent state spreads more and more. But its width is still of microscopic size if ∆t 1, i.e. t 12 tE . In more precise terms, the semi-classical measure of ψ (t) is still a Dirac measure at x (t) in that range of time. In our example 21 tE = 3.6. At a tim ...