TY - JOUR
T1 - Constructing Hamiltonian quantum theories from path integrals in a diffeomorphism-invariant context
AU - Ashtekar, Abhay
AU - Marolf, Donald
AU - Mourão, José
AU - Thiemann, Thomas
PY - 2000/12/7
Y1 - 2000/12/7
N2 - Osterwalder and Schrader introduced a procedure to obtain a (Lorentzian) Hamiltonian quantum theory starting from a measure on the space of (Euclidean) histories of a scalar quantum field. In this paper, we extend that construction to more general theories which do not refer to any background, spacetime metric (and in which the space of histories does not admit a natural linear structure). Examples include certain gauge theories, topological field theories and relativistic gravitational theories. The treatment is self-contained in the sense that an a priori knowledge of the Osterwalder-Schrader theorem is not assumed.
AB - Osterwalder and Schrader introduced a procedure to obtain a (Lorentzian) Hamiltonian quantum theory starting from a measure on the space of (Euclidean) histories of a scalar quantum field. In this paper, we extend that construction to more general theories which do not refer to any background, spacetime metric (and in which the space of histories does not admit a natural linear structure). Examples include certain gauge theories, topological field theories and relativistic gravitational theories. The treatment is self-contained in the sense that an a priori knowledge of the Osterwalder-Schrader theorem is not assumed.
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U2 - 10.1088/0264-9381/17/23/310
DO - 10.1088/0264-9381/17/23/310
M3 - Article
AN - SCOPUS:0034336443
SN - 0264-9381
VL - 17
SP - 4919
EP - 4940
JO - Classical and Quantum Gravity
JF - Classical and Quantum Gravity
IS - 23
ER -