These lecture notes aim at providing a purely analytical and accessible proof of the Callias index formula. In various branches of mathematics (particularly, linear and nonlinear partial differential operators, singular integral operators, etc.) and theoretical physics (e.g., nonrelativistic and relativistic quantum mechanics, condensed matter physics, and quantum field theory), there is much interest in computing Fredholm indices of certain linear partial differential operators. In the late 1970's, Constantine Callias found a formula for the Fredholm index of a particular first-order differential operator (intimately connected to a supersymmetric Dirac-type operator) additively perturbed by a potential, shedding additional light on the Fedosov-Hoermander Index Theorem. As a byproduct of our proof we also offer a glimpse at special non-Fredholm situations employing a generalized Witten index.
Publisher: Springer International Publishing AG ISBN: 9783319299761 Number of pages: 192 Weight: 3168 g Dimensions: 235 x 155 x 11 mm Edition: 1st ed. 2016
Simply reserve online and pay at the counter when you collect.
Available in shop from just two hours, subject to availability.
Thank you for your reservation
Your order is now being processed and we have sent a confirmation email to you at
This item can be requested from the shops shown below. If this item isn't available to be reserved nearby, add the item to your basket instead and select 'Deliver to my local shop' at the checkout, to be able to collect it from there at a later date.
When will my order be ready to collect?
Following the initial email, you will be contacted by the shop to confirm that your item is available for collection.
Call us on or send us an email at
Unfortunately there has been a problem with your order
Please try again or alternatively you can contact your chosen shop on or send us an email at