The Quantum Theory of General Relativity at Low Energies
... an old fallacy that effective Lagrangians can be used only at tree level. This sometimes still surfaces despite general knowledge to the contrary. “Effective field theory” is more than just the use of effective Lagangians. It implies a specific full field-theoretic treatment, with loops, renormaliza ...
... an old fallacy that effective Lagrangians can be used only at tree level. This sometimes still surfaces despite general knowledge to the contrary. “Effective field theory” is more than just the use of effective Lagangians. It implies a specific full field-theoretic treatment, with loops, renormaliza ...
PowerPoint - Subir Sachdev
... (In systems with Galilean invariance and at zero temperature, superfluid density=density of bosons always, independent of the strength of the interactions) ...
... (In systems with Galilean invariance and at zero temperature, superfluid density=density of bosons always, independent of the strength of the interactions) ...
B+ L Non-Conservation as a Semi
... the exponentiated external lines describe not vacuum to vacuum transitions, but configurations with particles in the initial and final states. In this case, there will be anti-Feynman pieces to the boundary conditions, and such terms may not be Wick rotated. The equation of motion resulting by varyi ...
... the exponentiated external lines describe not vacuum to vacuum transitions, but configurations with particles in the initial and final states. In this case, there will be anti-Feynman pieces to the boundary conditions, and such terms may not be Wick rotated. The equation of motion resulting by varyi ...
Electric Force Solutions
... 1. Three pithballs are suspended from thin threads. Various objects are then rubbed against other objects (nylon against silk, glass against polyester, etc.) and each of the pithballs is charged by touching them with one of these objects. It is found that pithballs 1 and 2 attract each other and tha ...
... 1. Three pithballs are suspended from thin threads. Various objects are then rubbed against other objects (nylon against silk, glass against polyester, etc.) and each of the pithballs is charged by touching them with one of these objects. It is found that pithballs 1 and 2 attract each other and tha ...
Gauge-Gravity Duality and the Black Hole Interior
... resolve the firewall question would be as follows: identify the field theory operator T^ dual to the matter energy momentum tensor T behind the horizon, and calculate its expectation value in any state. However, two severe problems present themselves. First, there is no simple dictionary for bu ...
... resolve the firewall question would be as follows: identify the field theory operator T^ dual to the matter energy momentum tensor T behind the horizon, and calculate its expectation value in any state. However, two severe problems present themselves. First, there is no simple dictionary for bu ...
PowerPoint
... charges on the surface of the material. This reduces the electric field within the bulk of the material. ...
... charges on the surface of the material. This reduces the electric field within the bulk of the material. ...
hw06_solutions
... The force on the segment of the loop closest to the wire is towards the wire, since the currents are in the same direction. The force on the segment of the loop farthest from the wire is away from the wire, since the currents are in the opposite direction. Because the magnetic field varies with dist ...
... The force on the segment of the loop closest to the wire is towards the wire, since the currents are in the same direction. The force on the segment of the loop farthest from the wire is away from the wire, since the currents are in the opposite direction. Because the magnetic field varies with dist ...
Final Review Honors Physics (14-15)
... (d) An electron is initially positioned 2.90 mm from the negative plate and released. What is the change in its potential energy when it reaches the positive plate? (-4.35×10-17 J) ...
... (d) An electron is initially positioned 2.90 mm from the negative plate and released. What is the change in its potential energy when it reaches the positive plate? (-4.35×10-17 J) ...
Casimir effect
In quantum field theory, the Casimir effect and the Casimir–Polder force are physical forces arising from a quantized field. They are named after the Dutch physicist Hendrik Casimir.The typical example is of two uncharged metallic plates in a vacuum, placed a few nanometers apart. In a classical description, the lack of an external field means that there is no field between the plates, and no force would be measured between them. When this field is instead studied using the QED vacuum of quantum electrodynamics, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force—either an attraction or a repulsion depending on the specific arrangement of the two plates. Although the Casimir effect can be expressed in terms of virtual particles interacting with the objects, it is best described and more easily calculated in terms of the zero-point energy of a quantized field in the intervening space between the objects. This force has been measured and is a striking example of an effect captured formally by second quantization. However, the treatment of boundary conditions in these calculations has led to some controversy.In fact, ""Casimir's original goal was to compute the van der Waals force between polarizable molecules"" of the metallic plates. Thus it can be interpreted without any reference to the zero-point energy (vacuum energy) of quantum fields.Dutch physicists Hendrik B. G. Casimir and Dirk Polder at Philips Research Labs proposed the existence of a force between two polarizable atoms and between such an atom and a conducting plate in 1947, and, after a conversation with Niels Bohr who suggested it had something to do with zero-point energy, Casimir alone formulated the theory predicting a force between neutral conducting plates in 1948; the former is called the Casimir–Polder force while the latter is the Casimir effect in the narrow sense. Predictions of the force were later extended to finite-conductivity metals and dielectrics by Lifshitz and his students, and recent calculations have considered more general geometries. It was not until 1997, however, that a direct experiment, by S. Lamoreaux, described above, quantitatively measured the force (to within 15% of the value predicted by the theory), although previous work [e.g. van Blockland and Overbeek (1978)] had observed the force qualitatively, and indirect validation of the predicted Casimir energy had been made by measuring the thickness of liquid helium films by Sabisky and Anderson in 1972. Subsequent experiments approach an accuracy of a few percent.Because the strength of the force falls off rapidly with distance, it is measurable only when the distance between the objects is extremely small. On a submicron scale, this force becomes so strong that it becomes the dominant force between uncharged conductors. In fact, at separations of 10 nm—about 100 times the typical size of an atom—the Casimir effect produces the equivalent of about 1 atmosphere of pressure (the precise value depending on surface geometry and other factors).In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon; in applied physics, it is significant in some aspects of emerging microtechnologies and nanotechnologies.Any medium supporting oscillations has an analogue of the Casimir effect. For example, beads on a string as well as plates submerged in noisy water or gas illustrate the Casimir force.