Quantum Field Theories in Curved Spacetime - Unitn
... a discrete “wedge reflection” isometry (this is automatic in the analytic case), ω must be (a) unique an (b) thermal (i.e. KMS) with respect to B with temperature given by the famous Hawking temperature: TH := κ/(2π), κ being the surface gravity of the black hole included in Kruskal spacetime. As a ...
... a discrete “wedge reflection” isometry (this is automatic in the analytic case), ω must be (a) unique an (b) thermal (i.e. KMS) with respect to B with temperature given by the famous Hawking temperature: TH := κ/(2π), κ being the surface gravity of the black hole included in Kruskal spacetime. As a ...
Renormalization group running of Newton`s constant G: The static
... that quantum gravitation, even though plagued by meaningless infinities in standard weak coupling perturbation theory, might actually make sense, and lead to a consistent theory at the nonperturbative level. As is often the case in physics, the best evidence does not come from often incomplete and p ...
... that quantum gravitation, even though plagued by meaningless infinities in standard weak coupling perturbation theory, might actually make sense, and lead to a consistent theory at the nonperturbative level. As is often the case in physics, the best evidence does not come from often incomplete and p ...
One-loop partition function of three
... values of the BMS charges. Only those diffeomorphisms which vanish sufficiently quickly at asymptotic infinity – in the sense that they do not change the values of these charges – are regarded as gauge transformations. One can then obtain the classical phase space by applying to the metric (2) the d ...
... values of the BMS charges. Only those diffeomorphisms which vanish sufficiently quickly at asymptotic infinity – in the sense that they do not change the values of these charges – are regarded as gauge transformations. One can then obtain the classical phase space by applying to the metric (2) the d ...
beyond space and time - Penn State University
... was missing. Because his calculations presuppose the classical spacetime of general relativity. Ashtekar: "Hawking did not complete Einstein's vision. He only treated matter and energy quantum mechanically." In quantum geometry however spacetime and so also the event horizon of a black hole are quan ...
... was missing. Because his calculations presuppose the classical spacetime of general relativity. Ashtekar: "Hawking did not complete Einstein's vision. He only treated matter and energy quantum mechanically." In quantum geometry however spacetime and so also the event horizon of a black hole are quan ...
Conceptual Issues in Canonical Quantum Gravity and Cosmology
... no final theory exists to date, so discussing conceptual issues in quantum gravity means to discuss them in existing approaches to such a theory. However, one can put forward various arguments in support of the generality of these issues in most approaches. This should become clear from the followin ...
... no final theory exists to date, so discussing conceptual issues in quantum gravity means to discuss them in existing approaches to such a theory. However, one can put forward various arguments in support of the generality of these issues in most approaches. This should become clear from the followin ...
Gravitation, the Quantum, and Cosmological Constant
... the entropy S, and the thermodynamic probability W allows us to draw conclusions about the total combinatorial factors defining W in terms of statistics of atoms or quanta. The positivity of (∆E)2 is strictly implied by the maximal value of the Boltzmann thermodynamic probability W at the state of t ...
... the entropy S, and the thermodynamic probability W allows us to draw conclusions about the total combinatorial factors defining W in terms of statistics of atoms or quanta. The positivity of (∆E)2 is strictly implied by the maximal value of the Boltzmann thermodynamic probability W at the state of t ...
Towards a quantum analog of weak KAM theory
... This paper proposes an extension of Mather’s variational principle [M1-2, M-F] and Fathi’s weak KAM theory [F1-3] to quantum states. We interpret “weak KAM” theory to mean the application of nonlinear PDE methods, mostly for first–order equations, towards understanding the structure of action minimiz ...
... This paper proposes an extension of Mather’s variational principle [M1-2, M-F] and Fathi’s weak KAM theory [F1-3] to quantum states. We interpret “weak KAM” theory to mean the application of nonlinear PDE methods, mostly for first–order equations, towards understanding the structure of action minimiz ...
Selberg zeta function and trace formula for the BTZ black hole
... [17]). On the other hand, the three-dimensional Bañados, Teitelboim, Zanelli (BTZ) black hole [1], [4], [5], [6], which is a solution of Einstein’s vacuum equation with a negative cosmological constant, has a Euclidean quotient presentation Γ\H3 for an appropriate Γ where, however, the fundamental ...
... [17]). On the other hand, the three-dimensional Bañados, Teitelboim, Zanelli (BTZ) black hole [1], [4], [5], [6], which is a solution of Einstein’s vacuum equation with a negative cosmological constant, has a Euclidean quotient presentation Γ\H3 for an appropriate Γ where, however, the fundamental ...
Document
... What we therefore have is a well defined theory of quantum gravity. Is this “THE” theory? Although this could only be settled in detail when the semiclassical limit is worked out, there are certain worries. The first one is the sort of action the Hamiltonian has. It only acts at vertices and it act ...
... What we therefore have is a well defined theory of quantum gravity. Is this “THE” theory? Although this could only be settled in detail when the semiclassical limit is worked out, there are certain worries. The first one is the sort of action the Hamiltonian has. It only acts at vertices and it act ...
Semiclassical formula for the number variance of the Riemann zeros
... numerical study, Odlyzko [4]showed that while short-range statistics (such as the distribution of the spacings E,,, - E, between neighbouring zeros) accurately conform to GUE predictions, long-range statistics (such as the correlations between distant spacings) do not, and are better described in te ...
... numerical study, Odlyzko [4]showed that while short-range statistics (such as the distribution of the spacings E,,, - E, between neighbouring zeros) accurately conform to GUE predictions, long-range statistics (such as the correlations between distant spacings) do not, and are better described in te ...
Quantum Transport and its Classical Limit
... Typical area enclosed in that time: sample area A. WL suppressed at flux F ~ hc/e through sample. Typical area enclosed in time terg: sample area A. Typical area enclosed in timetD: A(tD/terg)1/2. ...
... Typical area enclosed in that time: sample area A. WL suppressed at flux F ~ hc/e through sample. Typical area enclosed in time terg: sample area A. Typical area enclosed in timetD: A(tD/terg)1/2. ...
J JCAP01(2009)030 Covariant effective action for loop quantum cosmology `
... values for the states corresponding to realistic universes [6]. As expected, these non-singular trajectories do not exactly follow classical GR but correspond to a modified Friedman dynamics leading to a bounce at the value of the energy density predicted by the quantum theory and recovering classic ...
... values for the states corresponding to realistic universes [6]. As expected, these non-singular trajectories do not exactly follow classical GR but correspond to a modified Friedman dynamics leading to a bounce at the value of the energy density predicted by the quantum theory and recovering classic ...
A Brief Introduction into Quantum Gravity and Quantum Cosmology
... an expansion in D − 2 and use of renormalization-group (RG) techniques gives information about the behaviour in the vicinity of the non-trivial fixed point ...
... an expansion in D − 2 and use of renormalization-group (RG) techniques gives information about the behaviour in the vicinity of the non-trivial fixed point ...
Constructive Quantum Field Theory
... The pioneering work of early non-relativistic quantum theory led to the understanding that quantum dynamics on Hilbert space is a comprehensive predictive framework for microscopic phenomena. From the Bohr atom, through the nonrelativistic quantum theory of Schrödinger and Heisenberg, and the relat ...
... The pioneering work of early non-relativistic quantum theory led to the understanding that quantum dynamics on Hilbert space is a comprehensive predictive framework for microscopic phenomena. From the Bohr atom, through the nonrelativistic quantum theory of Schrödinger and Heisenberg, and the relat ...
GCOE13_5
... short distance quantum fluctuations are too large to absorb to the parameters of the particles. It means that the notion of point particle is no longer valid if we consider the quantum effects of gravity. In other words, if we want to include quantum gravity, we need to think about extended objects ...
... short distance quantum fluctuations are too large to absorb to the parameters of the particles. It means that the notion of point particle is no longer valid if we consider the quantum effects of gravity. In other words, if we want to include quantum gravity, we need to think about extended objects ...
1 Introduction and Disclaimer
... We will sketch the computation by Maulik and Okounkov of the quantum cohomology of Hilbn C2 . As you will see, the proof is somewhat indirect, but the methods used apply to general quiver varieties, and yield a variety of other great results. See [3] for a more direct proof. Due to limitations in sp ...
... We will sketch the computation by Maulik and Okounkov of the quantum cohomology of Hilbn C2 . As you will see, the proof is somewhat indirect, but the methods used apply to general quiver varieties, and yield a variety of other great results. See [3] for a more direct proof. Due to limitations in sp ...
quantum-gravity-presentation
... Quantum Gravity: Why so Difficult? • Don’t Buy the Tickets Quite Yet (III) • What Does it Mean to Have an Infinite Series with Terms of Increasing Dimension? • If You “Cutoff” the Series, You Can Apparently Fiddle with the Resulting Equations to Get Something With a Physical Meaning • But You Canno ...
... Quantum Gravity: Why so Difficult? • Don’t Buy the Tickets Quite Yet (III) • What Does it Mean to Have an Infinite Series with Terms of Increasing Dimension? • If You “Cutoff” the Series, You Can Apparently Fiddle with the Resulting Equations to Get Something With a Physical Meaning • But You Canno ...
Renormalisation of φ4-theory on noncommutative R4 to all orders
... always finite. The UV/IR-problem was found in all UV-divergent field theories on the Moyal plane. Models with at most logarithmic UV-divergences (such as two-dimensional and supersymmetric theories) can be defined at any loop order, but their amplitudes are still unbounded at exceptional momenta. ...
... always finite. The UV/IR-problem was found in all UV-divergent field theories on the Moyal plane. Models with at most logarithmic UV-divergences (such as two-dimensional and supersymmetric theories) can be defined at any loop order, but their amplitudes are still unbounded at exceptional momenta. ...
Information Processing with Quantum Gravity
... In general relativity, processes and events are causally non-separable because the causal structure of space-time geometry is non-fixed. In a non-fixed causality structure, the sequence of time steps has no interpretable meaning. In our macroscopic world, events and processes are distinguishable in ...
... In general relativity, processes and events are causally non-separable because the causal structure of space-time geometry is non-fixed. In a non-fixed causality structure, the sequence of time steps has no interpretable meaning. In our macroscopic world, events and processes are distinguishable in ...
Self-adjoint operators and solving the Schrödinger equation
... separately in their respective Hilbert spaces. This formula for the time-evolution of noninteracting quantum systems extends in an obvious way to systems consisting of an arbitrary finite number of non-interacting subsystems. In some cases where operators A and B don’t commute, one may instead use t ...
... separately in their respective Hilbert spaces. This formula for the time-evolution of noninteracting quantum systems extends in an obvious way to systems consisting of an arbitrary finite number of non-interacting subsystems. In some cases where operators A and B don’t commute, one may instead use t ...
Introduction to the general boundary formulation of quantum theory
... Usually a quantum system is encoded through a Hilbert space H of states and an operator algebra A of observables. This standard formulation of quantum theory has limitations that obstruct its application in a general relativistic context: Its operational meaning is tied to a background time. Its abi ...
... Usually a quantum system is encoded through a Hilbert space H of states and an operator algebra A of observables. This standard formulation of quantum theory has limitations that obstruct its application in a general relativistic context: Its operational meaning is tied to a background time. Its abi ...
Quantum Entanglement and the Geometry of Spacetime
... • quantum criticality • topological order • renormalization-group flows • energy conditions • many-body localization • quenches • much more… In general, difficult to compute—even in free theories Simplifies in certain theories with many strongly-interacting fields… ...
... • quantum criticality • topological order • renormalization-group flows • energy conditions • many-body localization • quenches • much more… In general, difficult to compute—even in free theories Simplifies in certain theories with many strongly-interacting fields… ...
On Water, Steam and String Theory
... This dependence of the renormalized temperature Tren (τ ) on a change of scale by eτ is what we call the “renormalization group flow” of Tren (τ ). The critical temperature Tc , at which the system is scale invariant, is called a fixed point of this flow. In Thermodynamics and in daily life one usua ...
... This dependence of the renormalized temperature Tren (τ ) on a change of scale by eτ is what we call the “renormalization group flow” of Tren (τ ). The critical temperature Tc , at which the system is scale invariant, is called a fixed point of this flow. In Thermodynamics and in daily life one usua ...
Solving quantum field theories via curved spacetimes
... that mediate color forces in those theories are analogues of photons, which mediate electromagnetic interactions. In contrast to uncharged photons, however, the gluons are themselves colored, and their number is N 2 − 1. Thus Neff is comparable to N 2. But large Neff alone is not enough to guarantee ...
... that mediate color forces in those theories are analogues of photons, which mediate electromagnetic interactions. In contrast to uncharged photons, however, the gluons are themselves colored, and their number is N 2 − 1. Thus Neff is comparable to N 2. But large Neff alone is not enough to guarantee ...