Mathematical Physics: A Modern Introduction to Its Foundations

"Ich kann es nun einmal nicht lassen, in diesem Drama von Mathematik und Physik-die sich im Dunkeln befruchten, aber von Angesicht zu Angesicht so gerne einander verkennen und vedeugnen-die RoUe des (wie ich geniigsam erfuhr, oft unerwiinschten) Boten zu spielen." Hermann Weyl It is said that mathematics is the language of Nature. If so, then physics is its poetry. Nature started to whisper into our ears when Egyptians and Babylonians were compelled to invent and use mathematics in their day-to-day activities. The faint geometric and arithmetical pidgin of over four thousand years ago, suitable for rudimentary conversations with nature as applied to simple landscaping, has turned into a sophisticated language in which the heart of matter is articulated. The interplay between mathematics and physics needs no emphasis. What may need to be emphasized is that mathematics is not merely a tool with which the presentation of physics is facilitated, but the only medium in which physics can survive. Just as language is the means by which humans can express their thoughts and without which they lose their unique identity, mathematics is the only language through which physics can express itself and without which.it loses its identity.