40352061
Quantum Field Theory in Curved Spacetime
I begin with an informal introduction to the subject of Quantum Field Theory in Curved Spacetime, indicating its status as an approximate theory, its basic physical effect, and its range of validity. I emphasize the importance of the Hawking effect, and of the fact that — while an approximation — the subject appears to admit a consistent mathematical and conceptual framework in its own right. After some brief historical and motivational remarks, I then outline such a suitable mathematical framework for the case of a linear field theory. Its principal elements are a suitable algebra and a suitable set of admissible states. The discussion of the latter incorporates recent work of R.M. Wald and the author. Evidence is given that this framework is complete, allows for the definition of a suitable energy-momentum tensor, and — through a result of R.M. Wald and the author — gives new insight into the Hawking effect. I end by stating two conjectures whose resolution may lead to a deeper understanding of the subject. I point out a close connection between these conjectures and a question posed by Fredenhagen and Haag in their recent axiomatic discussion of quantum gravity.
119686866
Classical and quantum scattering theory for linear scalar fields on the Schwarzschild metric I
We consider the covariant Klein-Gordon equation (□gg+m2) φ = 0 of mass m ≥ 0 on the exterior Schwarzschild spacetime of mass M. We introduce and study a set of outer and inner wave operators Ω0±, Ω1± (constructed in detail elsewhere) describing the asymptotic behavior of classical solutions—Ω0± for large distances and Ω1± near the Schwarzschild radius—as t→±∞. We re-interpret Ω1± on the Kruskal spacetime as solving a characteristic initial value problem for data on the future/past right horizon H±. As a by-product, we prove (since we require it here) a stronger result than previously known concerning the stability of the Schwarzschild black hole against linearized (scalar) perturbations. Using Ω0+, Ω1+ we construct in and out and horizon fields for the corresponding quantum problem. We give a construction for the Hartle-Hawking state ωH and prove that it coincides on the in and out fields with a state of exact thermal equilibrium in Minkowski space, while its two-point function on the (right) horizons H± is given (independently of m) by 
ωH[(δUo)(U1,ξ1)(δUo)(U2,ξ2)] = (−δ(ξ1,ξ2)/16φM2)(U1−U2−iϵ)−2 
(U1, U2ϵ (−∞, 0), ξ1, ξ2 ϵ S2) on H− and by a similar formula (with U→V, (−∞, 0) → (0, ∞), etc.) on H+. We also construct the Unruh state ωU as a product state, equal to the Minkowski vacuum on the in field, and with two-point function on H− equal to that given above for ωH. We prove that the restriction of this ωU to the out field coincides with a particular state of thermal radiation in Minkowski space. A special feature of our treatment is that we relate the horizon behavior of φ with the light-cone behavior of a massless free scalar field φ1 in a two-dimensional flat spacetime: 
δ2o1δT2−δ2o1δX2 = 0. 
 
 
In particular, using our classical characteristic-intial-value-problem results, we explain why the above expression for the two-point function of ∂Uφ on H is identical (modulo the trivial role played by S2 and up to a scale factor of 2M) with the well-known two-point function for ∂Uφ1 (U=T−X) on the null line T + X = 0.
120058153
Theorems on the uniqueness and thermal properties of stationary, nonsingular, quasifree states on spacetimes with a bifurcate killing horizon
Abstract This paper is concerned with the study of quasifree states of a linear, scalar quantum field in globally hyperbolic spacetimes possessing a one-parameter group of isometries with a bifurcate Killing horizon. Some results on the uniqueness and thermal properties of such states are well known in the special cases of Minkowski, Schwarzschild, and deSitter spacetimes, and our main aim is to present new stronger results and to generalize them to this wide class of spacetimes. As a preliminary to proving our theorems, we develop some aspects of the theory of globally of hyperbolic spacetimes with a bifurcate Killing horizon, we give some new results on the structure of Bose quasifree states of linear fields (the class which includes all the usual “Fock vacua”), and we clarify and further develop the notion of a “Hadamard state”. We then consider the quasifre e states on these spacetimes which have vanishing one-point function, are invariant under the one-parameter isometry group, and are nonsingular in a neighborhood of the horizon in the sense that their two-point function is of the Hadamard form there. We prove that, on a large subalgebra of observables (which are determined by observables localized in compact regions of the horizon) such states are unique and pure. Furthermore, if the spacetime admits a certain discrete “wedge reflection” isometry (as holds automatically in the analytic case) we prove that this state - if it exists - must be a KMS state at the Hawking temperature T = κ /2 π when restricted to those observables in our subalgebra which are localized in one of the (“right” or “left”) wedges of the spacetime where the Killing orbits are timelike near the horizon. Here, κ denotes the surface g ravity of the horizon. Under the further assumption that the nonsingularity of the state holds globally and that there are no “zero modes” in the one-partic le Hilbert space belonging to the state, we extend the uniqueness result to all observables localized in the full “domain of determinacy” of the hori zon. However, existence of states satisfying the hypotheses of our theorems does not hold in general and, indeed, we prove the nonexistence of any stationary (not necessarily quasifree) Hadamard state on the Schwarzschild-deSitter and Kerr spacetimes. We remark that nowhere in the analysis do we need to assume any form of Einstein's equations.
117461065
Mathematical aspects of the Hawking effect.
117120091
A uniqueness result for quantum field theory on spacetimes with bifurcate Killing horizons
123597708
A uniqueness result in the Segal–Weinless approach to linear Bose fields
We prove a theorem, which, while it fits naturally into the Segal–Weinless approach to quantization seems to have been overlooked in the literature: Let (D,σ) be a symplectic space, and T (t) a one parameter group of symplectics on (D,σ). Let (H, 2Im〈⋅ ‖ ⋅〉) be a complex Hilbert space considered as a real symplectic space, and U(t) a one‐parameter unitary group on H with strictly positive energy. Suppose there is a linear symplectic map K from D to H with dense range, intertwining T (t) and U(t). Then K is unique up to unitary equivalence.
328610
High-j single-particle neutron states outside the N=82 core
Abstract The behaviour of the i 13 / 2 and h 9 / 2 single-neutron strength was studied with the ( α , He 3 ) reaction on 138Ba, 140Ce, 142Nd and 144Sm targets at a beam energy of 51 MeV. The separation between the single-neutron states i 13 / 2 and h 9 / 2 was measured in N = 83 nuclei with changing proton number. To this end spectroscopic factors for states populated in high-l transfer were extracted from the data. Some mixing of l = 5 and 6 strength was observed with states that are formed by coupling the f 7 / 2 state to the 2 + and 3 − vibrational states and the mixing matrix elements were found to be remarkably constant. The centroids of the strength indicate a systematic change in the energies of the i 13 / 2 and h 9 / 2 single-neutron states with increasing proton number that is in quantitative agreement with the effects expected from the tensor interaction.
121267185
Properties of excited states in Ge77
The nucleus $^{77}\mathrm{Ge}$ was studied through the $^{76}\mathrm{Ge}(^{13}\mathrm{C},^{12}\mathrm{C})^{77}\mathrm{Ge}$ reaction at a sub-Coulomb energy. The angular distributions of $\ensuremath{\gamma}$ rays depopulating excited states in $^{77}\mathrm{Ge}$ were measured in order to constrain spin and parity assignments. Some of these assignments are of use in connection with neutrinoless double beta decay, where the population of states near the Fermi surface of $^{76}\mathrm{Ge}$ was recently explored using transfer reactions.
18182800
Population of positive-parity states in Sc 53 through one-proton knockout
The one-proton knockout reaction {sup 9}Be({sup 54}Ti,{sup 53}Sc+{gamma})X at 72 MeV/nucleon has been measured. The location of the first 3/2{sup -} state at 2110(3) keV was confirmed, and new {gamma}-ray transitions were observed at 1111(2), 1273(2), 1539(4), and 2495(5) keV. Large spectroscopic strength to excited states in {sup 53}Sc was found and attributed to the knockout of sd-shell protons.
41288355
Spectroscopy of the odd-odd fp-shell nucleus Sc-52 from secondary fragmentation
The odd-odd fp-shell nucleus {sup 52}Sc was investigated using in-beam {gamma}-ray spectroscopy following secondary fragmentation of a {sup 55}V and {sup 57}Cr cocktail beam. Aside from the known {gamma}-ray transition at 674(5) keV, a new decay at E{sub {gamma}}=212(3) keV was observed. It is attributed to the depopulation of a low-lying excited level. This new state is discussed in the framework of shell-model calculations with the GXPF1, GXPF1A, and KB3G effective interactions. These calculations are found to be fairly robust for the low-lying level scheme of {sup 52}Sc irrespective of the choice of the effective interaction. In addition, the frequency of spin values predicted by the shell model is successfully modeled by a spin distribution formulated in a statistical approach with an empirical, energy-independent spin-cutoff parameter.
119706030
Cross-shell excitations near the "island of inversion": Structure of Mg-30
Excited states in {sup 30}Mg have been populated to {approx}6{h_bar} and 5 MeV excitation energy with the {sup 14}C({sup 18}O,2p) reaction. Firm spin assignments for states with J>2{h_bar} have been made in this nucleus. The level scheme is compared to shell-model calculations using the Universal sd effective interaction and the Monte Carlo shell model method. Calculations employing a full sd model space fail to reproduce the observed levels. The results indicate that excitations across the N=20 gap are required at relatively low excitation energy to achieve a description of the data. The incorporation of the f{sub 7/2} and p{sub 3/2} orbitals into the model space gives improved results but indicate the need for further refinement of the models to reproduce the observed spectra.