Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.
Originating with the pioneering works of P. Fatou and G. Julia, the subject of complex dynamics has seen great advances in recent years. Complex dynamical systems often exhibit rich, chaotic behavior, which yields attractive computer generated pictures, for example the Mandelbrot and Julia sets, which have done much to renew interest in the subject. This self-contained book discusses the major mathematical tools necessary for the study of complex dynamics at an advanced level. Complete proofs of some of the major tools are presented; some, such as the Bers-Royden theorem on holomorphic motions, appear for the very first time in book format. An appendix considers Riemann surfaces and Teichmüller theory. Detailing the very latest research, the book will appeal to graduate students and researchers working in dynamical systems and related fields. Carefully chosen exercises aid understanding and provide a glimpse of further developments in real and complex one-dimensional dynamics.
I know you're alone . . . Shattered by her boyfriend's tragic death, Stacey is struggling in her first year of college, hoping that somehow, somewhere, Jacob is still alive. Now her nightmares are ba
A year has passed since Stacey Brown saved her best friend from a horrible death. Now she's having nightmares again, haunted by ghosts of the brutally murdered . . . and by a crazed stalker. As she de
What's your worst nightmare?For Ivy Jensen, it's the eyes of a killer that haunt her nights. For Parker Bradley, it's bloodthirsty sea serpents that slither in his dreams.And for seven essay contestan
THE FACTS Julian Roman, age sixteen, is an escapee from the Fairmount County Juvenile Detention Facility.His parents, Michael Roman and Jennifer Roman, are dead.Julian is wanted for murder.THE QUESTIO
I'll make you pay . . . School is over, and now Stacey, her boyfriend Jacob, and their friends have rented a beach cottage for the summer. No more stress, secrets, or stalkers. But then Stacey's nigh
Some secrets shouldn't be kept... Up until three months ago, everything in sixteen-year-old Camelia's life had been fairly ordinary: decent grades; an okay relationship with her parents; and
CAMELIA HAMMOND thought her powers of psychometry gave her only the ability to sense the future through touch. But now she has started to hear voices. Cruel voices. Berating her, telling her how ugly