Consider an algebraic variety, X which is a smooth algebraic manifold specified as the zero set of a known polynomial.
I would appreciate resource recommendations preferably or an outline of approaches as to how one can compute the period matrix of X, or more precisely, of the Jacobian variety...
Thanks, I see you what you mean. I will expand ##R_{\mu\nu\lambda\sigma}R^{\mu\nu\lambda\sigma}## and other curvature scalars in powers of ##h_{\mu\nu}##, and then find the terms that are required at tree-level for the amplitude to be reproduced.
I'm a physics student at university in the United Kingdom, and my research interests in particular include applications of differential and algebraic geometry in gauge field theories and string theory, though I do have wider interests in quantum field theory generally.
I look forward to...
Consider the action of a massive scalar field minimally coupled to gravity, that is,
$$S = \int d^4x \, \sqrt{-g} \, \left( 2\kappa^{-1} R + \partial_\mu \phi \partial^\mu \phi - m^2 \phi^2\right)$$
The theory I consider is canonically quantised gravity, with ##g_{\mu\nu} = \eta_{\mu\nu} +...