# Virtual Paricles and the Laws of Conservation

1. Sep 12, 2010

### filegraphy

Do virtual particles break the conservation laws? Thanks

2. Sep 13, 2010

### zhermes

No. Conservation of energy (i.e.) requires that the total amount of energy in the universe stays constant. If you take quantum mechanics into account, it might be better to phrase it as, 'the measured amount of energy in the universe must stay constant' (note that measurement doesn't just mean 'looking through a microscope and writing down a result, etc). Heisenberg's uncertainty principle states that the uncertainty in an energy measurement is related to the uncertainty in a time measurement:
$$\Delta E \Delta t \geq \bar{h}/2$$
Thus, virtual particles do not violate conservation of energy because the uncertainty in the energy of the system will always be large enough over the short time-periods under consideration.

3. Sep 13, 2010

### tom.stoer

Virtual particles in Feynman diagrams do not violate four-momentum conservation.The four-momentum is conserved at every vertex of the diagram. Virtual particles (inner lines) in Feynman diagrams violate the mass-shell condition E²-p² = m²; so a virtual photon can have non.zero m².That's one reason why it is called virtual.

Usually virtual particles do not violate other conservation laws. Especially a charge derived from a local gauge symmetry must be conserved in order to guarantuee consistency of the quantum gauge theory. This are the so-called Ward or Slavnov-Tayler identities, the "quantum generalization of the continuity equation".

Sometimes global symmetries are violated in quantum field theory; this is called an anomaly. One example is the axial anomaly where the axial current Ward identity is violated due to quantum effects. In this anomaly it's exactly one Feynman triangle diagram that creates the violation of the (global) axial symmetry. So there are special cases where one can say that virtual particles violate conservation laws.

4. Sep 13, 2010