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 May 6 awarded Commentator May 6 comment Why does work equal force times distance? @RonMaimon: Well, ok but what is Force? Mathematically it is a one form, you tell me what direction you want to move in and I tell you what force you are experiencing. In standard physics courses forces are of course drawn as vectors, but if you think about it, the direction of the force and the magnitude are really separate. What actually happens is: You or something else decides on a direction and then you get back the magnitude of force in that direction. One forms are naturally integrated along paths. May 6 revised Is the converse of Noether's first theorem true: Every conservation law has a symmetry? added 3 characters in body May 6 comment Is the converse of Noether's first theorem true: Every conservation law has a symmetry? This answer is wrong or at least imprecise. One should never accept arguments from authority. May 6 answered Is the converse of Noether's first theorem true: Every conservation law has a symmetry? May 6 revised Why does work equal force times distance? added 1 characters in body May 6 comment Why does work equal force times distance? So the answer to why force and distance is: You want to keep track of the change in potential energy. Infitesimally that change is determined by definition by $\vec F \cdot d\vec r$, now as you move along a path, you have to sum up (or integrate) those small contributions to get the total change in potential energy. Only in very simple circumstances the end result will literally be simply force times distance. May 6 comment Why does work equal force times distance? Well, I am not sure what you mean by $dV$. Indeed in standard mathematical notation, $dV = \partial_x V dx + \partial_y V dy + \partial_z V dz$ and physicists like to write this as $dV = \vec F \cdot d \vec r$. In words: The infinitesimal change in potential energy is the Force times the infinitesimal change in position. If you like that is the definition of a force. That definition might not be compatible with what you learned in your physics course. But it is the right definition for conservative forces. Non conservative forces like friction are a bit trickier. May 5 awarded Critic May 5 comment Feynman diagrams in effective theories Bjorn Wesen: There is, look for example at chapters 2 and 3 of Cvitanovics Field Theory notes: chaosbook.org/FieldTheory/pdf.html May 5 revised Why does work equal force times distance? added 184 characters in body May 5 answered Why does work equal force times distance? Apr 29 comment Poincare Symmetry in QFT To clarify: I am perfectly happy to accept that since space is almost flat, we can approximately neglect curvature. Similiarly how one can demonstrate that GR gives back Newtonian gravity in suitable limit. But in all other cases I know how to argue that these effects can be neglected, whereas in QFT some of the standard constructions seem to depend on the global structure of spacetime. This belief might be completely misguided, but I do want to understand why. Apr 29 comment Poincare Symmetry in QFT What I am really trying to understand is how the usual constructions can be sensible, although they do not exist in curved space (for example the S-Matrix). What is more, as I understood Poincare symmetry so far, it is a symmetry of an affine Space. I would expect translations to correspond to parallel transport along geodesics. To identify that with translations in the tangent space seems artificial. Some problems with QFT in curved space are outlined in: Christian Bär, Klaus Fredenhagen (Editors) Quantum Field Theory on Curved Spacetimes: Concepts and Mathematical Foundations Apr 25 awarded Supporter Apr 22 comment Poincare Symmetry in QFT Thank you for your answer. I do not understand your answer to my first question however. Do you mean by topological trivial, that it can be covered by a single coordinate chart? In that case you can certainly pull back the action of the poincare group, but this does not seem to yield a very geometric action. I thought that the right generalization was to consider the levi-civita connection, which at least gives you infitesimal translations. In any case we cannot apriori assume that spacetime is topological trivial. Apr 22 comment Poincare Symmetry in QFT My question is about neither, I want to understand QFT in a curved background. I will try to edit my question to clarify that. Apr 21 asked Poincare Symmetry in QFT Apr 10 answered Is the Lagrangian of a quantum field really a 'functional'? Apr 8 answered Could motives aid in the study of the Navier-Stokes equations?