The Quantum Structure of Space and Time (293 pages)

100 The Quantum Structure of Space and Time This allows us to write at = e--tH with H the Hamiltonian. In the case of a particle ...

Mathematical Structures 101 Quantization will associate a Hilbert space to this loop space. Roughly one can think of this Hilber ...

102 The Quantum Structure of Space and Time 4.1.3.3 Functorial description In the functorial description of conformal field theo ...

Mathematical Structures 103 4.1.3.4 Stringy geometry and T-dualaty Two-dimensional sigma models give a natural one-parameter def ...

104 The Quantum Structure of Space and Time Let us consider a particle or a string on a space-time that is given by a n- dimensi ...

Mathematical Structures^105 4.1.3.5 Topological string theory In the case of point particles it was instructive to consider the ...

106 The Quantum Structure of Space and Time A-model topological strings give an important example of a typical stringy gen- eral ...

Mathematical Structures 107 mirror symmetry will interchange the A-model with the B-model. A famous exam- ple of the power of mi ...

108 The Quantum Structure of Space and Time 4.1.4.1 Summing over string topologies First, we want to generalize to the situation ...

Mathematical Structures 109 through the formalism of D-branes [22] these can be analyzed exactly in string perturbation theory. ...

(^110) The Quantum Structure of Space and Time In general the topological string partition function (of the A model) takes the f ...

Mathematical Structures 111 terms of pictures we have (i) the statistical model, (ii) the so-called limit space, that captures t ...

(^112) The Quantum Structure of Space and Time 4.1.5 D-branes As we have mentioned, the crucial ingredient to extend string theo ...

Mathematical Structures^113 4.1.5.1 Branes and matrices One of the most remarkable facts is that D-branes can be given a multipl ...

114 The Quantum Structure of Space and Time the brane charge p(E) that can be considered as a class in H*(X). (For convenience w ...

Mathematical St~~ctu7.e~^115 4.1.5.4 Non-perturbative dualities We indicated that in M-theory we do not want to include only str ...

116 The Quantum Structure of Space and Time Computing the BPS states through geometric quantization we find that abrane(p) = H*( ...

Mathematical Structures 117 0 One could also question whether we are looking for a single overarching math- ematical structure o ...

118 The Quantum Structure of Space and Time [lo] Z. Bern, L. J. Dixon and D. A. Kosower, N = 4 super-Yang-Mills theory, QCD and ...

Mathematical Structures^119 4.2 Discussion G. Horowitz At the very beginning you asked: what is quantum geometry? You said it sh ...