Negative energy densities in integrable quantum field theories at
... An a priori question is what form the stress-energy tensor T αβ takes in these models. There is a straightforward answer in models derived from a classical Lagrangian, such as the sinh-Gordon model, where a candidate for the operator can be computed [FMS93, KM93, MS94]. However, we also consider the ...
... An a priori question is what form the stress-energy tensor T αβ takes in these models. There is a straightforward answer in models derived from a classical Lagrangian, such as the sinh-Gordon model, where a candidate for the operator can be computed [FMS93, KM93, MS94]. However, we also consider the ...
Q - UTA HEP WWW Home Page
... twice its weight in order to ensure sufficient attraction, compute the required electric field strength near the surface of the drum. The electric force must be the same as twice the gravitational force on the toner particle. So we can write Fe ...
... twice its weight in order to ensure sufficient attraction, compute the required electric field strength near the surface of the drum. The electric force must be the same as twice the gravitational force on the toner particle. So we can write Fe ...
SUMMER HOLIDAYS HOME-WORK
... 29. (a) Depict the equipotential surfaces for a system of two identical positive point charges placed a distance ‘d’ apart.(b) Deduce the expression for the potential energy of a system of two point charges q1 andq2brought from infinity to the points r1andr2 respectively in the presence of external ...
... 29. (a) Depict the equipotential surfaces for a system of two identical positive point charges placed a distance ‘d’ apart.(b) Deduce the expression for the potential energy of a system of two point charges q1 andq2brought from infinity to the points r1andr2 respectively in the presence of external ...
Homework #4 Chapter 24 Capacitance
... potential difference across the capacitor plates? (b) What plate radius is required if the positively charged plate is to have a charge of 10.0 µC? Picture the Problem The potential difference V across a parallel-plate capacitor, the electric field E between its plates, and the separation d of the p ...
... potential difference across the capacitor plates? (b) What plate radius is required if the positively charged plate is to have a charge of 10.0 µC? Picture the Problem The potential difference V across a parallel-plate capacitor, the electric field E between its plates, and the separation d of the p ...
Counting energy packets in the electromagnetic
... 2. The concept of wave energy packet in the classic approach The synchronous oscillations of the electric and magnetic fields result in periodical oscillations of wave energy density. An observer using an electric antenna and a wire loop to probe these fields detects short time windows when either p ...
... 2. The concept of wave energy packet in the classic approach The synchronous oscillations of the electric and magnetic fields result in periodical oscillations of wave energy density. An observer using an electric antenna and a wire loop to probe these fields detects short time windows when either p ...
Problems Chapter 9
... have choosen a phase for basis vectors this choice is valid for every linear combination. There is one more subtle point. When we write Σ matrices in the usual form we have in effect done a choice of phases, for example Σy has purely imaginary elements, how this combine with the above freedom in pha ...
... have choosen a phase for basis vectors this choice is valid for every linear combination. There is one more subtle point. When we write Σ matrices in the usual form we have in effect done a choice of phases, for example Σy has purely imaginary elements, how this combine with the above freedom in pha ...
Nonlinear Propagation of Crossing Electromagnetic Waves in
... not even indirectly. In fact, two possible strategies can be used for the quest of 77 scattering. On one hand, the cross section for the process will be maximum at a possible future photon-photon collider[5], based on an electron laser producing two beams of photons in the MeV range (i.e., having wa ...
... not even indirectly. In fact, two possible strategies can be used for the quest of 77 scattering. On one hand, the cross section for the process will be maximum at a possible future photon-photon collider[5], based on an electron laser producing two beams of photons in the MeV range (i.e., having wa ...
The Parallel Plate Capacitor
... capacitor and the effect of placing dielectric materials between the plates of the capacitor. Theory A capacitor consisting of two parallel metal plates each with an area A, and separated by a distance d, can be shown to have a capacitance C: ...
... capacitor and the effect of placing dielectric materials between the plates of the capacitor. Theory A capacitor consisting of two parallel metal plates each with an area A, and separated by a distance d, can be shown to have a capacitance C: ...
the quantum vacuum
... evidence, relates to an omnipresent reality which, in contrast to the ideas of „nothingness“, „void“ or „empty space“, as they are inherent in the classical concept, has the status of a „physical system“ with well defined, but uncommon, properties. The reality of the vacuum, as it is envisioned by q ...
... evidence, relates to an omnipresent reality which, in contrast to the ideas of „nothingness“, „void“ or „empty space“, as they are inherent in the classical concept, has the status of a „physical system“ with well defined, but uncommon, properties. The reality of the vacuum, as it is envisioned by q ...
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.