![]() ![]() This procedure runs into some problems which are widely discussed in the literature. Traditional way to construct the dressed propagator of UP is the Dyson summation which introduces the width and redefines the mass of UP. Some aspects of the abovementioned problems are considered further in more detail. It should be noted that the PS definition of the mass and width is connected with the structure of the dressed propagator. One of the PS definitions, where mass and width follow from the parametrization, is known as complex-mass definition. However, it does not define the mass and width in unique way. The PS provides gauge invariant definition and make it possible to solve the problem of threshold singularity. Moreover, at one loop in the conventional OMS, the problem of threshold singularity arises which originates from the wave-function renormalization constant. It was shown that OMS scheme contains spurious higher-order gauge-dependent terms. There has been considerable discussion concerning definition of the vector-boson mass. In the pole scheme (PS), the definitions of mass and width are based on the complex-valued position of the propagator pole. The on-mass-shell (OMS) scheme defines the mass and width of UP by the renormalization of the self-energy amplitude. Two standard definitions of the mass and width of unstable particles (UP), which are usually considered in the literature, have different nature. We obtain the propagators in modified Breit-Wigner forms which correspond to the complex-mass definition. The expressions for the dressed propagators of unstable vector and spinor fields are derived in an analytical way for this case. Spectral function is found for a special case when the propagator of scalar unstable particle has Breit-Wigner form. If you don't use slug & pounds you need to modify F = m * a to be something like F = k * m * a where k is a unitless scaling constant equal to 1/32 to adjust the result so that 1 pound mass under standard gravity produces 1 pound-force.The propagators of unstable particles are considered in framework of the convolution representation. Because of this there is a unit called a slug that is used for mass where a 1 slug mass will accelerate at 1 ft/s^2 when a 1 pound force is applied and using this a 1 slug mass will produce 32 pound-force under standard gravity. When you are dealing with science you usually have to be more precise about the terms you use because you can be dealing with conditions that are not as simple as you standing on a stationary scale in a doctors office where.įor pounds it is considered a unit of mass and can be used as force, also referred to as the pound-force, but that causes confusion with formula like F = m * a for example if you have a 1 pound (mass) object accelerated by gravity at 32 ft/s^2 you have a force of 32 pounds (force) but a 1 pound mass produces a 1 pound-force force under standard gravity. Since the conversion between mass and weight is fairly constant for every day activities they have been used fairly interchangeably. That's what makes science and math so great is that it explains why things like this, that initially sound counterintuitive, are actually correct. It's because the earth curves that the ships will drop below a point where they can be seen.) ![]() ![]() (If you are having trouble seeing this just imagine the horizon and how ships can go 'over' it. If you could throw a baseball fast enough, it would circle the earth because the farther the ball goes forward the further down "ground" is since the earth is curved, if you would move in a straight line the ground would eventually recede beneath you. ![]() Just because it never reaches ground doesn't mean it isn't falling toward that ground.Įssentially, an object in orbit means that object is constantly falling toward another object (an object in orbit around Earth constantly falls toward Earth), but because it is also moving sideways (and not just straight down, imagine throwing a ball how it moves 2 directions: down and in the direction you threw it) then it never actually hits the ground. ![]()
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