author={Florian Conrady and Carlo Rovelli},
  journal={International Journal of Modern Physics A},
We investigate the idea of a "general boundary" formulation of quantum field theory in the context of the Euclidean free scalar field. We propose a precise definition for an evolution kernel that propagates the field through arbitrary space–time regions. We show that this kernel satisfies an evolution equation which governs its dependence on deformations of the boundary surface and generalizes the ordinary (Euclidean) Schrodinger equation. We also derive the classical counterpart of this… 
From the discrete to the continuous: towards a cylindrically consistent dynamics
Discrete models usually represent approximations to continuum physics. Cylindrical consistency provides a framework in which discretizations exactly mirror the continuum limit. As a standard tool for
On the Covariant Hamilton-Jacobi Equation for the Teleparallel Equivalent of General Relativity
The covariant Hamilton-Jacobi equation for the Teleparallel Equivalent of General Relativity is derived based on the analysis of constraints within the De Donder-Weyl covariant Hamiltonian theory
Spin foam propagator: A new perspective to include the cosmological constant
In recent years, the calculation of the first non-vanishing order of the metric 2-point function or graviton propagator in a semiclassical limit has evolved as a standard test for the credibility of
Holomorphic quantization of linear field theory in the general boundary formulation
We present a rigorous quantization scheme that yields a quantum field theory in general boundary form starting from a linear field theory. Following a geometric quantization approach in the Kahler
Second-order amplitudes in loop quantum gravity
We explore some second-order amplitudes in loop quantum gravity. In particular, we compute some second-order contributions to diagonal components of the graviton propagator in the large distance
0 60 40 44 v 2 1 3 M ay 2 00 6 Graviton propagator in loop quantum gravity
We compute some components of the graviton propagator in loop quantum gravity, using the spinfoam formalism, up to some second order terms in the expansion parameter.
Semiclassical analysis of loop quantum gravity
In this Ph.D. thesis, we explore and develop new methods that should help in determining an effective semiclassical description of canonical loop quantum gravity and spin foam gravity. A brief
Graviton propagator in loop quantum gravity
We compute some components of the graviton propagator in loop quantum gravity, using the spinfoam formalism, up to some second-order terms in the expansion parameter.


Techniques and Applications of Path Integration
Partial table of contents: Probabilities and Probability Amplitudes for Paths. Correspondence Limit for the Path Integral (Heuristic). Vector Potentials and Another Proof of the Path Integral
Space-Time Approach to Non-Relativistic Quantum Mechanics
Non-relativistic quantum mechanics is formulated here in a different way. It is, however, mathematically equivalent to the familiar formulation. In quantum mechanics the probability of an event which
Quantum Electrodynamics. I. A Covariant Formulation
Attempts to avoid the divergence difficulties of quantum electrodynamics by multilation of the theory have been uniformly unsuccessful. The lack of convergence does indicate that a revision of
Schrödinger's cat and the clock: lessons for quantum gravity
I review basic principles of the quantum mechanical measurement process in view of their implications for a quantum theory of general relativity. It turns out that a clock as an external classical
An Introduction to spin foam models of quantum gravity and BF theory
In loop quantum gravity we now have a clear picture of the quantum geometry of space, thanks in part to the theory of spin networks. The concept of ‘spin foam’ is intended to serve as a similar
Wave functions constructed from an invariant sum over histories satisfy constraints.
This paper shows for a wide class of theories, including gauge theories, general relativity, and first-quantized string theories, that wave functions constructed from a sum over histories are, in fact, annihilated by the constraints.
Minkowski vacuum in background independent quantum gravity
We consider a local formalism in quantum field theory, in which no reference is made to infinitely extended spacial surfaces, infinite past or infinite future. This can be obtained in terms of a
Quantum Electrodynamics
THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To